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Start Over Subject commutative semigroup

1. Simple zeropotent paramedial groupoids are balanced

Creator:
Bashir, Robert El, Ježek, Jraoslav, and Kepka, Tomáš
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
math, commutative semigroup, and invariant congruence
Language:
English
Description:
This short note is a continuation of and and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of [4].
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The rank of a commutative semigroup

Creator:
Cegarra, Antonio M. and Petrich, Mario
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
semigroup, commutative semigroup, independent subset, rank, separative semigroup, power cancellative semigroup, and archimedean component
Language:
English
Description:
The concept of rank of a commutative cancellative semigroup is extended to all commutative semigroups S by defining rank S as the supremum of cardinalities of finite independent subsets of S. Representing such a semigroup S as a semilattice Y of (archimedean) components Sα, we prove that rank S is the supremum of ranks of various Sα. Representing a commutative separative semigroup S as a semilattice of its (cancellative) archimedean components, the main result of the paper provides several characterizations of rank S; in particular if rank S is finite. Subdirect products of a semilattice and a commutative cancellative semigroup are treated briefly. We give a classification of all commutative separative semigroups which admit a generating set of one or two elements, and compute their ranks.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public