Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
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TL;DR: In this article, it was shown that for each idempotent e∈J a, there exists an ideme-potent f ∈ J b such that f = ≦e.
Abstract: In this paper we prove the following: Let S be a regular semigroup anda, bany elements of S such that J b = ≦ J a . Then, for each idempotent e∈J a , there exists an idempotent f∈ J b such that f = ≦e .
15 citations
14 citations
TL;DR: In this paper, a lattice-ordered ring of real functions of a frame L and its subclasses LSC(L) and USC(LSC) of lower and upper semicontin- uous real functions is studied.
14 citations
TL;DR: It is proved that all maximal subgroups of the free idempotent generated semigroup over a band B are free for all B belonging to a band variety V if and only if V consists either of left seminormal bands, or of right semin formal bands.
Abstract: We prove that all maximal subgroups of the free idempotent generated semigroup over a band B are free for all B belonging to a band variety V if and only if V consists either of left seminormal bands, or of right seminormal bands.
14 citations
14 citations