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On the Zeroid Radical of FUCHS for Semigroups

โœ Scribed by Harbans Lal

Publisher
John Wiley and Sons
Year
1974
Tongue
English
Weight
300 KB
Volume
60
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

This short note introduces a radical in semigroups with zero, similar to L. FUCHS' Zeroid Radical for rings [l]. We prove here that the zeroid radical of a semigroup with zero is the intersection of a certain number of prinie ideals; nil and zeroid radicals coincide in N-semigroups; and also under special circumstances, the factor semigroups S = S -R, where R is the zeroid radical of X, is free of both left and right zero divisor ideals.

Throughout this note, X will denote a semigroup with zero. An element n. in S is called a left zero divisor if there is a non-zero y in S such that L * y = 0. If every element of an ideal (always two-sided) of X is a left zero divisor, we shall call it a left zero divisor ideal. An ideal M of X is called a maximal left zero divisor ideal, if there exists no left zero divisor ideal containing A

๐Ÿ“œ SIMILAR VOLUMES

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I n this note we shall indicate the usefulness of the concepts of q-elements and HOEHNKE'S O-radical by characterizing certain semigroups containing q-elements. I n particular, we characterize completely the left cancellative semigroups with q-elements. We shall also show that the importance of O-ra

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โœ D. R. Latorre ๐Ÿ“‚ Article ๐Ÿ“… 1970 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 156 KB

In studying the algebraic structure of semigroups, H. J. HOEHNKE in [I] and [a] has used respresentations of a semigroup S by transformations on a set to introduce a radical, rad S , as a certain congruence on S , and an associated ideal rado S of S , called the 0-radical of S. An internal characte