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Congruences on ideal nil-extension of completely regular semigroups

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Chinese Science Bulletin 1998年第5期43卷 379-381页

作者： REN Xueming 1, 2 GUO Yuqi 2 and CEN Jiaping (Shum Kar-ping) 31. Department of Mathematics, Xi’an University of Architecture & Technology, Xi’an 710055, China 2. Department of Mathematics, Yunnan University, Kunming 650091, China 3. Department of Department of Mathematics Xi’an University of Architecture & Technology Xi’an China Department of Mathematics Yunnan University Kunming China Department of Mathematics Chinese University of Hong Kong Hong Kong

Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?

关键词： completely regular semigroups ideal nil-extension congruences.

The right dual of left C-rpp semigroups

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Chinese Science Bulletin 1997年第19期42卷 1599-1603页

作者： GUO YuqiDepartment of Mathematics, Yunnan University, Kunming 650091, China Department of Mathematics Yunnan University Kunming China

SEMIGROUP S is said to be rpp (dually, lpp) if every principal right ideal aS^1(S^1a) of S, re-garded as a right (left)S^1-system, is projective. The semigroup which is both rpp and lpp is said to be abundant. These kinds of generalized regular semigroups have aroused wideattention. The Green’s,relations (~*-Green’s relations introduced by Pastijn) have formed avery useful tool in study on regular (abundant) semigroups. In order to develop the study onrpp semigroups a step further, we introduced the so-called (1)-Green’s,relation which

关键词： rpp semigroups left (right) C-rpp semigroups. (I)-Green’s relations.

π-inverse semigroups Whose Lattice of π-inverse Subsemigroups is ∧- semidistributive

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数学进展 1998年第4期 76-77页

作者：田振际

ＡｓｅｍｉｇｒｏｕｐＳｉｓｃａｌｅｄπ－ｒｅｇｕｌａｒｉｆｆｏｒｅｖｅｒｙｅｌｅｍｅｎｔａｏｆＳｔｈｅｒｅｅｘｉｓｔｓｍ∈Ｚ＋（ｔｈｅｓｅｔｏｆｐｏｓｉｔｉｖｅｉｎｔｅｇｅｒｓ）ｓｕｃｈｔｈａｔａｍｉｓｒｅｇｕｌａｒ... 详细信息

ＡｓｅｍｉｇｒｏｕｐＳｉｓｃａｌｅｄπ－ｒｅｇｕｌａｒｉｆｆｏｒｅｖｅｒｙｅｌｅｍｅｎｔａｏｆＳｔｈｅｒｅｅｘｉｓｔｓｍ∈Ｚ＋（ｔｈｅｓｅｔｏｆｐｏｓｉｔｉｖｅｉｎｔｅｇｅｒｓ）ｓｕｃｈｔｈａｔａｍｉｓｒｅｇｕｌａｒ．Ｌｅｔｕｓｄｅｎｏｔｅｂｙｒ（ａ...

关键词： inverse semigroups Subsemigroups Whose Lattice is of

A generalized Clifford theorem of semigroups

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Science China Mathematics 2010年第10期53卷 1097-1101页

作者： SHUM K.P. Department of Mathematics The University of Hong Kong

A U-abundant semigroup S in which every H-class of S contains an element in the set of projections U of S is said to be a U-superabundant *** is an analogue of regular semigroups which are unions of groups and an analogue of abundant semigroups which are *** 1941,Clifford proved that a semigroup is a union of groups if and only if it is a semilattice of completely simple *** years later,Fountain generalized this result to the class of superabundant *** this paper,we extend their work to U-superabundant semigroups.

关键词： Clifford theorem unions of groups superabundant semigroups U-abundant semigroups Usuperabundant semigroups

Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive semigroups

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Advances in Pure Mathematics 2014年第6期4卷 244-252页

作者： Hongbo Liu Yi Li School of Science Southwest University of Science and Technology Mianyang China

Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.

关键词： Hybrid Iterative Algorithm Uniformly Asymptotically Nonexpansive semigroups Equilibrium Problem Common Fixed Point

Generating Set of the Complete semigroups of Binary Relations

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Applied Mathematics 2016年第1期7卷 98-107页

作者： Yasha Diasamidze Neset Aydin Ali Erdoğan Shota Rustavelli University Batumi Georgia Ç anakkale Onsekiz Mart University &Ccedil anakkale Turkey Hacettepe University Ankara Turkey

Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .

关键词： semigroups Binary Relation Generated Set Generators

Analyticity of semigroups generated by Degenerate Mixed Differential Operators

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Advances in Pure Mathematics 2011年第3期1卷 42-48页

作者： Adel Saddi 不详

In this paper we are interested in studying the dissipativity of degenerate mixed differential operators involving an interface point. We show that, under particular interface conditions, such operators generate analy... 详细信息

关键词： Adjoint Interface Dissipative Operators Analytic semigroups

An Iterative Algorithm for Generalized Mixed Equilibrium Problems and Fixed Points of Nonexpansive semigroups

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Journal of Applied Mathematics and Physics 2017年第2期5卷 276-293页

作者： Jong Kyu Kim Salahud din Won Hee Won Hee Department of Mathemarics Education Kyungnam University Changwon Gyeongnam Korea Department of Mathematics Jazan University Jazan Kingdom of Saudi Arabia

In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and gener... 详细信息

关键词： Meir-Keeler Contraction Mappings Left Regular Generalized Mixed Equilibrium Problems Variational Inequalities α-Inverse Strongly Monotone Mappings Nonexpansive semigroups

Zappa-Szép Products of semigroups

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Applied Mathematics 2015年第6期6卷 1047-1068页

作者： Suha Wazzan Mathematics Department King Abdulaziz University Jeddah Saudi Arabia

The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from actions of two semigroups on one another satisfying axiom derived by G. Zappa. We illustrate the correspondence between the two versions internal and the external of Zappa-Szép products of semigroups. We consider the structure of the internal Zappa-Szép product as an enlargement. We show how rectangular band can be described as the Zappa-Szép product of a left-zero semigroup and a right-zero semigroup. We find necessary and sufficient conditions for the Zappa-Szép product of regular semigroups to again be regular, and necessary conditions for the Zappa-Szép product of inverse semigroups to again be inverse. We generalize the Billhardt λ-semidirect product to the Zappa-Szép product of a semilattice E and a group G by constructing an inductive groupoid.

关键词： Inverse semigroups Groups Semilattice Rectangular Band Semidiret Regular Enlargement Inductive Groupoid