منابع مشابه
FREE SEMIGROUPS AND IDEMPOTENTS IN T
The known theory for an oid T shows how to find a subset T of ?T, which is a compact right topological semigroup [I]. The success of the methods in [2] for obtaining properties of-T has prompted us to see how successful they would be in another context. Thus we find (Theorem 4.8) that T cont ains copies of free semigroups on 2? generators, is an immediate consequence of the stronger resu...
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Our paper is inspired by the paper [3] by M. Nathanson, in which he considers iteration of the process of adjoining identities or zeros to semigroups and characterizes the resulting semigroup in the case when one starts with the trivial semigroup. We consider also the third type of adjoining, namely, we adjoin idempotents “that behave like some already existing elements.” We investigate the pro...
متن کاملIdempotents in Compact Semigroups and Ramsey Theory
We shall show here that van der Waerden’s theorem on arithmetic progressions and its variants, the Hales-Jewett theorem ([HJ]), the theorem of T. J. Carlson and S. G. Simpson ([CS]), and the theorem of T. J. Carlson (theorem 2 of [C]), can be obtained by an analysis of idempotents in compact semigroups. We obtain in this way a sharpening of Carlson’s result (which provides an “infinite” version...
متن کاملFundamental Semigroups Having a Band of Idempotents
The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider are weakly B-abundant and satisfy the congruence condition (C). Any orthodox semigroup S with E(S) ...
متن کاملSemigroups whose idempotents form a subsemigroup ∗
We prove that every semigroup S in which the idempotents form a sub-semigroup has an E-unitary cover with the same property. Furthermore, if S is E-dense or orthodox, then its cover can be chosen with the same property. Then we describe the structure of E-unitary dense semigroups. Our results generalize Fountain's results on semigroups in which the idempotents commute, and are analogous to thos...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1972
ISSN: 0097-3165
DOI: 10.1016/0097-3165(72)90021-0