In this paper, the concept of C-left hyperideals is introduced in ordered semihypergroups, and several related properties are investigated. In particular, we discuss the relationships between the greatest left hyperid...In this paper, the concept of C-left hyperideals is introduced in ordered semihypergroups, and several related properties are investigated. In particular, we discuss the relationships between the greatest left hyperideals and C-left hyperideals of ordered semihypergroups. Furthermore, we introduce the concept of left bases of an ordered semihypergroup, and give out the sufficient and necessary conditions of the existence of the greatest C-left hyperideal of an ordered semihypergroup by the properties of left bases. The result about C-left ideals in ordered semigroups is generalized to the ordered semihypergroups.展开更多
In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore,we introduce the concepts of weakly prime, qu...In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore,we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasiprime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover, we give some characterizations of weakly quasiprime left hyperideals by the left hyperideals and weakly m-systems. We also characterize the quasi-prime left hyperideals in terms of the m-systems. In particular, we prove that an ordered semihypergroup S is strongly semisimple if and only if every left hyperideal of S is the intersection of all quasi-prime left hyperideals of S containing it.展开更多
In this paper we introduce derivations in hyperlatices and derive some basic properties of them. Also, some properties of differential hyperideals and differential hypercongruences are studied. Further we prove that f...In this paper we introduce derivations in hyperlatices and derive some basic properties of them. Also, some properties of differential hyperideals and differential hypercongruences are studied. Further we prove that for an injective strong differential hyperlattice（L, d） and for a strongly differential hypercongruence R of（L, d）, the quotient hyperlattice（L/R, g） is an injective strongly differential hyperlattice, where g is an injective strong derivation on L/R induced by d.展开更多
We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distrib...We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)-semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propose some lemmas and theorems on homomorphism, congruence relation, quotient (m, n)-semihyperring, etc. and prove these theorems. We further extend it to introduce the relationship between fuzzy sets and (m, n)-semihyperrings and propose fuzzy hyperideals and homomorphism theorems on fuzzy (m, n)-semihyperrings and the relationship between fuzzy (m, n)-semihyperrings and the usual (m, n)-semihyper-rings.展开更多
In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasne...In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.展开更多
基金The NSF(11271040,11361027)of Chinathe Key Project(2014KZDXM055)of Department of Education of Guangdong Province+1 种基金the University Natural Science Project(KJ2015A161)of Anhui Provincethe NSF(2014A030313625)of Guangdong Province
文摘In this paper, the concept of C-left hyperideals is introduced in ordered semihypergroups, and several related properties are investigated. In particular, we discuss the relationships between the greatest left hyperideals and C-left hyperideals of ordered semihypergroups. Furthermore, we introduce the concept of left bases of an ordered semihypergroup, and give out the sufficient and necessary conditions of the existence of the greatest C-left hyperideal of an ordered semihypergroup by the properties of left bases. The result about C-left ideals in ordered semigroups is generalized to the ordered semihypergroups.
基金Supported by the National Natural Science Foundation of China(Grant No.11361027)the University Natural Science Project of Anhui Province(Grant No.KJ2015A161)+1 种基金the Natural Science Foundation of Guangdong Province(Grant No.2014A030313625)the Key Project of Department of Education of Guangdong Province(Grant No.2014KZDXM055)
文摘In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore,we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasiprime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover, we give some characterizations of weakly quasiprime left hyperideals by the left hyperideals and weakly m-systems. We also characterize the quasi-prime left hyperideals in terms of the m-systems. In particular, we prove that an ordered semihypergroup S is strongly semisimple if and only if every left hyperideal of S is the intersection of all quasi-prime left hyperideals of S containing it.
基金Supported by the National Natural Science Foundation of China(Grant No.11571281)
文摘In this paper we introduce derivations in hyperlatices and derive some basic properties of them. Also, some properties of differential hyperideals and differential hypercongruences are studied. Further we prove that for an injective strong differential hyperlattice（L, d） and for a strongly differential hypercongruence R of（L, d）, the quotient hyperlattice（L/R, g） is an injective strongly differential hyperlattice, where g is an injective strong derivation on L/R induced by d.
文摘We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)-semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propose some lemmas and theorems on homomorphism, congruence relation, quotient (m, n)-semihyperring, etc. and prove these theorems. We further extend it to introduce the relationship between fuzzy sets and (m, n)-semihyperrings and propose fuzzy hyperideals and homomorphism theorems on fuzzy (m, n)-semihyperrings and the relationship between fuzzy (m, n)-semihyperrings and the usual (m, n)-semihyper-rings.
基金supported by a Grant of National Natural Science Foundation of China(Grant Nos.11461025and 11561023)
文摘In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.
