Let S be a semigroup and let A be an S-act. Some necessary and sufficient conditions that S-subacts of A are maximal S-subacts are given. A relation B which is similar to the Green relation in semigroups is defined. B...Let S be a semigroup and let A be an S-act. Some necessary and sufficient conditions that S-subacts of A are maximal S-subacts are given. A relation B which is similar to the Green relation in semigroups is defined. By the relation B, it is proved that a non-empty set L of A is a maximal S-subact if and only if A／L is a （maximal） B-class. Finally, the concept of a C-subact is defined, some properties of C-subacts are discussed, and it is proved that A contains no maximal S-subacts if and only if every cyclic S-subact of A is a C-subact. Consequently, the results obtained by Imrich Fabrici that semigroups contain no maximal （left） ideals are the corollary of this paper.展开更多
In this paper we introduce a class of right S-acts called retractable S-acts which are right S-acts with homomorphisms into their all subacts. We also give some classifications of monoids by comparing such acts with f...In this paper we introduce a class of right S-acts called retractable S-acts which are right S-acts with homomorphisms into their all subacts. We also give some classifications of monoids by comparing such acts with flatness properties.展开更多
Effective design of nanoheterostructure anode with high ion/electron migration kinetics can give electrode with superior electrochemical performance.However,the design and preparation of nanoheterostructure composites...Effective design of nanoheterostructure anode with high ion/electron migration kinetics can give electrode with superior electrochemical performance.However,the design and preparation of nanoheterostructure composites with high-capacity and long cycling life in half and pouch full cells remain a big challenge.Here,a novel micro-pore MnS/Mn_(2)SnS_(4)heterostructure nanowire were in situ encapsulated into the N and S elements co-doped amorphous carbon tubes(abbreviated as(MnS/Mn_(2)SnS_(4))@N,S-ACTs)and showed superior energy storage properties in Na-/Li-ion half cells and pouch full cells.The Na-/Li-storage capabilities improvement are attribute to the strong synergistic effect between MnS/Mn_(2)SnS_(4)heterostructure and N,S-ACTs protective layer,the former induces an local built-in electric field between Mn_(2)Sn S_(4)and MnS during charging/discharging,accelerating interfacial ion/electron diffusion dynamics,the latter effective maintains the morphology and volume evolution during Na~+/Li~+charging/discharging,achieving a long-term cycling stability(e.g.,high discharge capacity of 79.2 mAh/g with the capacity retention of 79.3%can be gained after 2200 cycles at 3 C in(Mn S/Mn_(2)Sn S_(4))@N,S-ACTs//LiFePO_(4)pouch full cells;a high capacity of~34 mAh/g at 10 C can be got with a Coulombic efficiency of 100%after 1000 cycles in pouch(Mn S/Mn_(2)Sn S_(4))@N,S-ACTs//Na_(3)V_(2)(PO_(4))_(2)O_(2)F full cells.展开更多
This paper investigates the characterizations of monoids over which all strongly flat right S-acts are regular. It is shown that all strongly flat right S-acts are regular if and only if S is a right PSF monoid and ev...This paper investigates the characterizations of monoids over which all strongly flat right S-acts are regular. It is shown that all strongly flat right S-acts are regular if and only if S is a right PSF monoid and every left collapsible submonoid of S contains a left zero. This result gives a new answer to the problem in Kilp and Knauer.展开更多
LetS be a semigroup andE the set of all idempotents inS. LetS-Act be the category of allS-acts. LetC be a full subcategory ofS-Act which containss S and is closed under coproducts and summands. It is proved that, inC,...LetS be a semigroup andE the set of all idempotents inS. LetS-Act be the category of allS-acts. LetC be a full subcategory ofS-Act which containss S and is closed under coproducts and summands. It is proved that, inC, anS-actP is projective and unitary if and only ifP? ? j? I Se i ,e i ?E. In particular,P is a projective, indecomposable and unitary object if and only ifP ?Se for somee ∈E. These generalize some results obtained by Knauer and Talwar.展开更多
基金The National Natural Science Foundation of China(No10626012), Jiangsu Planned Projects for Postdoctoral ResearchFund(No0502022B)
文摘Let S be a semigroup and let A be an S-act. Some necessary and sufficient conditions that S-subacts of A are maximal S-subacts are given. A relation B which is similar to the Green relation in semigroups is defined. By the relation B, it is proved that a non-empty set L of A is a maximal S-subact if and only if A／L is a （maximal） B-class. Finally, the concept of a C-subact is defined, some properties of C-subacts are discussed, and it is proved that A contains no maximal S-subacts if and only if every cyclic S-subact of A is a C-subact. Consequently, the results obtained by Imrich Fabrici that semigroups contain no maximal （left） ideals are the corollary of this paper.
文摘In this paper we introduce a class of right S-acts called retractable S-acts which are right S-acts with homomorphisms into their all subacts. We also give some classifications of monoids by comparing such acts with flatness properties.
基金financial support from the project funded by National Natural Science Foundation of China(Nos.52372188,51902090)2023 Introduction of studying abroad talent program,Science Technology Program of Jilin Province(No.20220508141RC)+5 种基金the 111 Project(No.B13013)China Postdoctoral Science Foundation(No.2019M652546)Henan Province Postdoctoral Start-Up Foundation(No.1901017)Henan Normal University Doctoral Start-Up Project Foundation,“111”project(No.D17007)Henan Center for Outstanding Overseas Scientists(No.GZS2018003)the Dalian Revitalization Talents Program(No.2022RG01)。
文摘Effective design of nanoheterostructure anode with high ion/electron migration kinetics can give electrode with superior electrochemical performance.However,the design and preparation of nanoheterostructure composites with high-capacity and long cycling life in half and pouch full cells remain a big challenge.Here,a novel micro-pore MnS/Mn_(2)SnS_(4)heterostructure nanowire were in situ encapsulated into the N and S elements co-doped amorphous carbon tubes(abbreviated as(MnS/Mn_(2)SnS_(4))@N,S-ACTs)and showed superior energy storage properties in Na-/Li-ion half cells and pouch full cells.The Na-/Li-storage capabilities improvement are attribute to the strong synergistic effect between MnS/Mn_(2)SnS_(4)heterostructure and N,S-ACTs protective layer,the former induces an local built-in electric field between Mn_(2)Sn S_(4)and MnS during charging/discharging,accelerating interfacial ion/electron diffusion dynamics,the latter effective maintains the morphology and volume evolution during Na~+/Li~+charging/discharging,achieving a long-term cycling stability(e.g.,high discharge capacity of 79.2 mAh/g with the capacity retention of 79.3%can be gained after 2200 cycles at 3 C in(Mn S/Mn_(2)Sn S_(4))@N,S-ACTs//LiFePO_(4)pouch full cells;a high capacity of~34 mAh/g at 10 C can be got with a Coulombic efficiency of 100%after 1000 cycles in pouch(Mn S/Mn_(2)Sn S_(4))@N,S-ACTs//Na_(3)V_(2)(PO_(4))_(2)O_(2)F full cells.
基金the National Natural Science Foundation of China(10171082)and by NWNU-KJCXGC212
文摘This paper investigates the characterizations of monoids over which all strongly flat right S-acts are regular. It is shown that all strongly flat right S-acts are regular if and only if S is a right PSF monoid and every left collapsible submonoid of S contains a left zero. This result gives a new answer to the problem in Kilp and Knauer.
基金Research partially supported by a UGC (HK) (Grant No. 2160092)
文摘LetS be a semigroup andE the set of all idempotents inS. LetS-Act be the category of allS-acts. LetC be a full subcategory ofS-Act which containss S and is closed under coproducts and summands. It is proved that, inC, anS-actP is projective and unitary if and only ifP? ? j? I Se i ,e i ?E. In particular,P is a projective, indecomposable and unitary object if and only ifP ?Se for somee ∈E. These generalize some results obtained by Knauer and Talwar.
