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Upper and Lower Periodic Subsets of Semigroups.
- Source :
-
Algebra Colloquium . Sep2011, Vol. 18 Issue 3, p447-460. 14p. - Publication Year :
- 2011
-
Abstract
- In this paper, a new topic about a vast class of subsets of semigroups and binary systems, which contains all ideals, periodic subsets and sub-semigroups, is introduced and studied. In fact, the 'upper periodic subsets' can be considered as a generalization of the conception 'ideals'. We prove a fundamental theorem which states that if A is a (left) upper B-periodic subset of a semigroup S, then under some conditions, it has a unique direct representation $A=\mathfrak{B}\cdot D\,\dot{\cup}\,B^1\cdot E$, where B1=B ∪ {1} and B ⊆ 픅 ≤ S. Especially, we prove a unique direct representation for upper and lower T-periodic subsets, and classify all sub-semigroups of S containing a fixed element T to three classes. This classification gives us more interesting properties for the real semigroups. At last, we characterize upper and lower T-periodic subsets of semigroups and groups. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10053867
- Volume :
- 18
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Algebra Colloquium
- Publication Type :
- Academic Journal
- Accession number :
- 62534743
- Full Text :
- https://doi.org/10.1142/S1005386711000332