By Kar Ping Shum, Zhe-Xian Wan, Jiping Zhang

ISBN-10: 9812382607

ISBN-13: 9789812382603

On Normalized desk Algebras Generated via a devoted Non-Real portion of measure three (Z Arad & G Chen); Graph Semigroups (V Dlab & T Pospichal); Moor-Penrose Generalized Inverses of Matrices Over department jewelry (Z-X Wan); M-Solid Pseudovarieties and Galois Connections (K Denecke & B Pibaljommee); Indecomposable Decompositions of CS-Modules (J L Gomez Pardo & P A Guil Asensio); Hereditary earrings, QF2 earrings and earrings of Finite illustration style (C R Hajarnavis); sturdy Burst errors Detecting Cyclic Codes (S Jain); at the Homology Bifunctors Over Semimodules (X T Nguyen); a few difficulties and Conjectures in Modular Representations (J-P Zhang); and different papers

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**Additional resources for Advances in algebra : proceedings of the ICM Satellite Conference in Algebra and Related Topics**

**Example text**

Proof. We will prove only the assertion concerning the condition (( c = zcycz)). The remaining cases can be proved similarly. Let S satisfies the condition (( c = zcycz)) and let a E Y be an arbitrary element. For any a E S, there exists z, y , z E S such that a = xayaz, and we have that z E Sp, y E S, and z E 5'6, for some p , y , b E Y . By a E S, and a = xayaz it follows that ap = a y = a6 = a , so a = z a y a z = z ( z a y a z ) y ( z a y a z ) z= = (z'ay)a( zyz)a(yaz') = (z'ay) (zayaz)( z y z ) a ( y a z ' ) = = (z%yz)a( yaz' yz) a(yaz') E s,as,as,.

Semigroups satisfying some of these conditions were studied only from the ideal-theoretical point of view, by S. Lajos and G. The purpose of this paper is to describe the structure and give some new ideal-theoretical characterizations of these semigroups. 1. Introduction The notion of the regularity in semigroups and rings was introduced by J. von Neumann in 1131, 1936, and his work initiated investigation of many other types of the regularity. Left, right and complete regularity were introduced and studied by A.

Lajos and G. Szdsz in [ll],1975. In [4], S. Bogdanovib, M. Cirib, P. StanimiroviC: and T. PetkoviC considered a more general problem and determined all types of the regularity of semigroups and their elements determined by linear equations, where linear equations are defined as follows. For a given alphabet A , by A+ the free semigroup over A is denoted. Let X be a countable alphabet whose elements are called variables, and let c be a symbol such that c $! X , called a constant. By L we denote the set of all words u 6 (X U { c } ) + satisfying the following conditions: - the constant c appears at least once in u, - at least one of the variables appears in u, - any variable appears at most once in u.

### Advances in algebra : proceedings of the ICM Satellite Conference in Algebra and Related Topics by Kar Ping Shum, Zhe-Xian Wan, Jiping Zhang

by Donald

4.5