DIMONOIDS

作者：Zhuchok A V^*

来源：Algebra and Logic, 2011, 50(4): 323-340.

• dimonoid
• dimonoid with commutative operation
• free commutative dimonoid
• semilattice of subdimonoids
• semigroup

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.

• 出版日期2011-9