In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and re...In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and relator sets for , and then proved some finite and infinite cases about it. In this paper, by considering the product, we show Green’s relations L and R as well as we present the conditions for this product to be left cancellative, orthodox and finally left (right) inverse(s).展开更多
Under some conditions, the special congruences of partial abelian monoid are those induced by the special ideals, and a class of special ideals of partial abelian monoid has some upper and lower bound properties.
An element of a semigroup S is called irreducible if it cannot be expressedas a product of two elements in S both distinct from itself. In this paper we showthat the class C of all completely regular monoids with irre...An element of a semigroup S is called irreducible if it cannot be expressedas a product of two elements in S both distinct from itself. In this paper we showthat the class C of all completely regular monoids with irreducible identity elementssatises the strong isomorphism property and so it is globally determined.展开更多
A limit variety is a variety that is minimal with respect to being non-finitely based.Since the turn of the millennium,much attention has been given to the classification of limit varieties of aperiodic monoids.Seven ...A limit variety is a variety that is minimal with respect to being non-finitely based.Since the turn of the millennium,much attention has been given to the classification of limit varieties of aperiodic monoids.Seven explicit examples have so far been found,and the task of locating other examples has recently been reduced to two subproblems,one of which is concerned with monoids that satisfy the identity asat asatc.We provide a complete solution to this subproblem by showing that there are precisely two limit varieties that satisfy this identity.One of them turns out to be the first example having infinitely many subvarieties.It is also deduced that the variety generated by any monoid of order 5 or less contains at most countably many subvarieties.展开更多
Weak Hopf algebra is defined. The aim of this work is to study the relations between the weak antipode of a weak Hopf algelra and the monoid of group like elements. At first, the author shows some properties of weak ...Weak Hopf algebra is defined. The aim of this work is to study the relations between the weak antipode of a weak Hopf algelra and the monoid of group like elements. At first, the author shows some properties of weak Hopf algebras. And, for some weak Hopf algebras, some properties of the weak antipodes are given if the monoids of group like elements are inverse or orthodox semigroups. At end, the author gets a weak Hopf algebra whose monoid of group like elements is regular.展开更多
In this paper, we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter-Drinfeld modules over a weak braided Hopf monoid. We apply the gener...In this paper, we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter-Drinfeld modules over a weak braided Hopf monoid. We apply the general result to the calculus of the center in module categories.展开更多
In this paper,we give a suficient condition under which an involution monoid generates a variety with continuum many subvarieties.According to this result,several involution J-trivial monoids are shown to generate var...In this paper,we give a suficient condition under which an involution monoid generates a variety with continuum many subvarieties.According to this result,several involution J-trivial monoids are shown to generate varieties with continuum many subvarieties.These examples include Rees quotients of free involution monoids,Lee monoids with involution,and Straubing monoids with involution.展开更多
We find on a monoid M the complex-valued solutions f,g:M→C such that f is central and g is continuous of the functional equation f(xσ(y))+f(τ(y)x)=2f(x)g(y),x,y∈M,whereσ:M→M is an involutive automorphism andτ:M...We find on a monoid M the complex-valued solutions f,g:M→C such that f is central and g is continuous of the functional equation f(xσ(y))+f(τ(y)x)=2f(x)g(y),x,y∈M,whereσ:M→M is an involutive automorphism andτ:M→M is an involutive anti-automorphism.The solutions are described in terms of multiplicative functions,additive functions and characters of2-dimensional representations of M.展开更多
An endomorphism monoid of an algebra A.is said to be a band if every endomorphism on A is an idempotent,and it is said to be a demi-band if every noninject ive endomorphism on A is an idempotent.We precisely determine...An endomorphism monoid of an algebra A.is said to be a band if every endomorphism on A is an idempotent,and it is said to be a demi-band if every noninject ive endomorphism on A is an idempotent.We precisely determine finite Kleene algebras whose endomorphism monoids are demi-bands and bands via Priestley duality.展开更多
In this paper, we find the orders of the Renner monoids for J-irreducible monoids K＊p（G）, where G is a simple algebraic group over an algebraically closed field K, and p ： G → GL（V） is the irreducible represent...In this paper, we find the orders of the Renner monoids for J-irreducible monoids K＊p（G）, where G is a simple algebraic group over an algebraically closed field K, and p ： G → GL（V） is the irreducible representation associated with the highest root.展开更多
The paper introduces a class of inverse(sub)monoids which contains Jones-Lawson’s gauge inverse(sub)monoid.The aim is to give examples and the basic properties of these monoids.Jones-Lawson’s gauge inverse monoid,as...The paper introduces a class of inverse(sub)monoids which contains Jones-Lawson’s gauge inverse(sub)monoid.The aim is to give examples and the basic properties of these monoids.Jones-Lawson’s gauge inverse monoid,as an inverse submonoid of the polycyclic monoid,is the prototype in our development line.The generalization leads also to Mea-kin-Sapir type results involving bijections between special congruences and special wide inverse submonoids.展开更多
In this paper we first present a combinatorial characterization of an inverse monoid of a graph. Then using this we prove that a bipartite graph with an inverse monoid is uniquely K_2, and that a graph G has an invers...In this paper we first present a combinatorial characterization of an inverse monoid of a graph. Then using this we prove that a bipartite graph with an inverse monoid is uniquely K_2, and that a graph G has an inverse monoid if and only if the join of G and a complete graph also has an inverse monoid.展开更多
Structural mapping is an important method for studying algebraic structures.Hom-algebra and monoidal Hom-group are new structures produced by algebra and group structural mappings,respectively.These structures are imp...Structural mapping is an important method for studying algebraic structures.Hom-algebra and monoidal Hom-group are new structures produced by algebra and group structural mappings,respectively.These structures are important algebra and group generalizations and are closely related to them.Let(A,β)be a Hom-algebra and(G,α)a monoidal Hom-group.A structure of(A,β)graded by(G,α)is introduced;this structure is called Hom-group graded algebra.This study presents the definition of Hom group graded algebra,provides some examples,and dis-cusses its basic properties.Furthermore,a sufficient and necessary condition that makes(A,β)a strongly(G,α)-graded algebra is explored using a structure mapβand unit 1A.Finally,by using different maps,two sufficient and necessary conditions for a Hom-algebra to be a(G,α)-graded algebra are expressed in different ways.展开更多
三I推理方法是一种新的模糊推理方法,通过已有的研究成果表明,在许多方面它优于传统的CRI推理方法,它将成为模糊系统和人工智能的理论和应用研究中一个比较理想的推理机制。最近,国外学者提出了一个新的模糊逻辑形式系统,叫做Monoidal t...三I推理方法是一种新的模糊推理方法,通过已有的研究成果表明,在许多方面它优于传统的CRI推理方法,它将成为模糊系统和人工智能的理论和应用研究中一个比较理想的推理机制。最近,国外学者提出了一个新的模糊逻辑形式系统,叫做Monoidal t-norm based logics(简记为MTL),已经证明这个形式系统是所有基于左连续三角范数的模糊逻辑的共同形式化。本文基于这类逻辑将三I推理方法形式化,从而在这些逻辑系统中为三推理方法找到了可靠的逻辑依据。展开更多
文摘In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and relator sets for , and then proved some finite and infinite cases about it. In this paper, by considering the product, we show Green’s relations L and R as well as we present the conditions for this product to be left cancellative, orthodox and finally left (right) inverse(s).
基金supported by Research Fund of Kumoh National Institute of Technology, Korea
文摘Under some conditions, the special congruences of partial abelian monoid are those induced by the special ideals, and a class of special ideals of partial abelian monoid has some upper and lower bound properties.
基金The NSF(11261021) of Chinathe NSF(20142BAB201002) of Jiangxi Province
文摘An element of a semigroup S is called irreducible if it cannot be expressedas a product of two elements in S both distinct from itself. In this paper we showthat the class C of all completely regular monoids with irreducible identity elementssatises the strong isomorphism property and so it is globally determined.
基金supported by the Ministry of Science and Higher Education of the Russian Federation(FEUZ-2023-0022)supported by the National Natural Science Foundation of China(12271224,12171213,11771191)+1 种基金Fundamental Research Funds for the Central Universities(lzujbky-2023-ey06)Natural Science Foundation of Gansu Province(20JR5RA275).
文摘A limit variety is a variety that is minimal with respect to being non-finitely based.Since the turn of the millennium,much attention has been given to the classification of limit varieties of aperiodic monoids.Seven explicit examples have so far been found,and the task of locating other examples has recently been reduced to two subproblems,one of which is concerned with monoids that satisfy the identity asat asatc.We provide a complete solution to this subproblem by showing that there are precisely two limit varieties that satisfy this identity.One of them turns out to be the first example having infinitely many subvarieties.It is also deduced that the variety generated by any monoid of order 5 or less contains at most countably many subvarieties.
文摘Weak Hopf algebra is defined. The aim of this work is to study the relations between the weak antipode of a weak Hopf algelra and the monoid of group like elements. At first, the author shows some properties of weak Hopf algebras. And, for some weak Hopf algebras, some properties of the weak antipodes are given if the monoids of group like elements are inverse or orthodox semigroups. At end, the author gets a weak Hopf algebra whose monoid of group like elements is regular.
基金Supported by Ministerio de Ciencia e Innovación,project MTM2010-15634Supported by FEDER
文摘In this paper, we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter-Drinfeld modules over a weak braided Hopf monoid. We apply the general result to the calculus of the center in module categories.
基金supported by the National Natural Science Foundation of China(Nos.12271224,12171213,11771191)the Fundamental Research Funds for the Central Universities(No.lzujbky-2023-ey06)the Natural Science Foundation of Gansu Province(No.20JR5RA275).
文摘In this paper,we give a suficient condition under which an involution monoid generates a variety with continuum many subvarieties.According to this result,several involution J-trivial monoids are shown to generate varieties with continuum many subvarieties.These examples include Rees quotients of free involution monoids,Lee monoids with involution,and Straubing monoids with involution.
基金Supported by the National Science Foundation of China(Grant Nos.12061059 and 61763041)。
文摘We find on a monoid M the complex-valued solutions f,g:M→C such that f is central and g is continuous of the functional equation f(xσ(y))+f(τ(y)x)=2f(x)g(y),x,y∈M,whereσ:M→M is an involutive automorphism andτ:M→M is an involutive anti-automorphism.The solutions are described in terms of multiplicative functions,additive functions and characters of2-dimensional representations of M.
文摘An endomorphism monoid of an algebra A.is said to be a band if every endomorphism on A is an idempotent,and it is said to be a demi-band if every noninject ive endomorphism on A is an idempotent.We precisely determine finite Kleene algebras whose endomorphism monoids are demi-bands and bands via Priestley duality.
基金the National Natural Science Foundation of China （No. 10471116）.
文摘In this paper, we find the orders of the Renner monoids for J-irreducible monoids K＊p（G）, where G is a simple algebraic group over an algebraically closed field K, and p ： G → GL（V） is the irreducible representation associated with the highest root.
文摘The paper introduces a class of inverse(sub)monoids which contains Jones-Lawson’s gauge inverse(sub)monoid.The aim is to give examples and the basic properties of these monoids.Jones-Lawson’s gauge inverse monoid,as an inverse submonoid of the polycyclic monoid,is the prototype in our development line.The generalization leads also to Mea-kin-Sapir type results involving bijections between special congruences and special wide inverse submonoids.
文摘In this paper we first present a combinatorial characterization of an inverse monoid of a graph. Then using this we prove that a bipartite graph with an inverse monoid is uniquely K_2, and that a graph G has an inverse monoid if and only if the join of G and a complete graph also has an inverse monoid.
基金The National Natural Science Foundation of China (No. 12271089, 12471033)。
文摘Structural mapping is an important method for studying algebraic structures.Hom-algebra and monoidal Hom-group are new structures produced by algebra and group structural mappings,respectively.These structures are important algebra and group generalizations and are closely related to them.Let(A,β)be a Hom-algebra and(G,α)a monoidal Hom-group.A structure of(A,β)graded by(G,α)is introduced;this structure is called Hom-group graded algebra.This study presents the definition of Hom group graded algebra,provides some examples,and dis-cusses its basic properties.Furthermore,a sufficient and necessary condition that makes(A,β)a strongly(G,α)-graded algebra is explored using a structure mapβand unit 1A.Finally,by using different maps,two sufficient and necessary conditions for a Hom-algebra to be a(G,α)-graded algebra are expressed in different ways.
文摘三I推理方法是一种新的模糊推理方法,通过已有的研究成果表明,在许多方面它优于传统的CRI推理方法,它将成为模糊系统和人工智能的理论和应用研究中一个比较理想的推理机制。最近,国外学者提出了一个新的模糊逻辑形式系统,叫做Monoidal t-norm based logics(简记为MTL),已经证明这个形式系统是所有基于左连续三角范数的模糊逻辑的共同形式化。本文基于这类逻辑将三I推理方法形式化,从而在这些逻辑系统中为三推理方法找到了可靠的逻辑依据。
