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
On lower radicals of semigroups
โ Scribed by Eqbal Ahmed; Richard Wiegandt
- Publisher
- John Wiley and Sons
- Year
- 1973
- Tongue
- English
- Weight
- 257 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0025-584X
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๐ SIMILAR VOLUMES
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 s
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