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- Title
Dimonoids.
- Authors
Zhuchok, A.
- Abstract
It is proved that a system of axioms for a dimonoid is independent and Cayley's theorem for semigroups has an analog in the class of dimonoids. The least separative congruence is constructed on an arbitrary dimonoid endowed with a commutative operation. It is shown that an appropriate quotient dimonoid is a commutative separative semigroup. The least separative congruence on a free commutative dimonoid is characterized. It is stated that each dimonoid with a commutative operation is a semilattice of Archimedean subdimonoids, each dimonoid with a commutative periodic semigroup is a semilattice of unipotent subdimonoids, and each dimonoid with a commutative operation is a semilattice of a-connected subdimonoids. Various dimonoid constructions are presented.
- Subjects
AXIOMS; CAYLEY numbers (Algebra); REPRESENTATIONS of semigroups; ABELIAN semigroups; MONOIDS; GROUP theory
- Publication
Algebra & Logic, 2011, Vol 50, Issue 4, p323
- ISSN
0002-5232
- Publication type
Article
- DOI
10.1007/s10469-011-9144-7