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Title: 條件B1を滿足する単純準群
Other Titles: A Simple Semigroup Satisfying condition B1 / 条件B1を満足する単純準群
Authors: 江口, 俊男
Authors (alternative): Eguchi, Toshio
Issue Date: 28-Feb-1957
Publisher: 長崎大学学芸学部
Citation: 長崎大学学芸学部自然科学研究報告. vol.6, p.1-4; 1957
Abstract: In this paper we shall show that dssuming condition B1 it is easy to prove the existence of idempotents in S-N and to prove the so called "Complets simplicity" of S. Condition B1 : S is a semigroup with the kerner N having at least one N-potent simple left and at least one N-potent simple right ideal. Then we can prove five important theorems (1) Let S be a simple semigroup satisfying Condition B1. Then to every a∈S-N there exist two elements e,f∈S-N with a=ea, a=af Moreover : for every a, b, x, y ∈S-N the following implications hold : a=xb→b= xa a=by→b=ay with x,y ∈S-N (2) The elements e and f of (1) are idempotents. (3) Let S be a simple semigroup Satisfying Conditions B1. Then every simple left ideal L of S is of the form L=N+Se, where e is an idempotent ∈L-N Analogously, every right simple ideal R of S has the form R=N+fs, where f is an idempotent ∈R-N (4) Let S be a simple semigroup satisfying Condition B1. Let L be a simple left ideal of S. Then L is a semigroup having the following properties : a) It has least one right identity e ∈L-N for every element ∈L-N. b) Every idempotent e*∈L-N is a right identity for every element ∈L-N. c) In L it is possible to cancel on the right with eyery element c for which e.c non ∈N holds. (5) A simple semigroup satisfying Condition B1 is completely simple.
URI: http://hdl.handle.net/10069/33292
ISSN: 05471419
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 6

Citable URI : http://hdl.handle.net/10069/33292

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