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One-sided principal ideals in the direct product of two semigroups

Imrich Fabrici (1993)

Mathematica Bohemica

A necessary and sufficient condition is given for a) a principal left ideal L ( s , t ) in S × T to be equal to the direct product of the corresponding principal left ideals L ( s ) × L ( t ) , b) an -class L ( s , t ) to be equal to the direct product of the corresponding -classes L s × L t .

Principal ideals of finitely generated commutative monoids

José Carlos Rosales, Juan Ignacio García-García (2002)

Czechoslovak Mathematical Journal

We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.

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