✦ LIBER ✦

On 0-Radical of a Semigroup

✍ Scribed by M. Satyanarayana

Publisher: John Wiley and Sons
Year: 1975
Tongue: English
Weight: 208 KB
Volume: 66
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19750660123

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✦ Synopsis

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-radical cannot be over-emphasized because it happens to be trivial or zero in many nice semigroups. According to LA TORRE [a], an element x in a semigroup S is called a g-element if xmb = xnc for every b, c E S and for some integers m, n 2 0. If m or n is 0, then we assume xos = s. I n the works of HOEHNKE [l] and SEIDEL [3], one finds that RadO S , called the 0-radical of a semigroup S , is a maximal yuasiregular ideal i.e., an ideal which is maximal with respect to the property that every element of it is a q-element. This is explicitely stated by LA TORRE [2]. By making simple observations from lemmas 1.2 and 1.3 of SEIDEL [3], we have

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