On Some Properties for Cofiniteness of Submonoids and Ideals of an Affine Semigroup

Abstract

Let S and C be affine semigroups in Nd such that S⊆C. We provide a characterization for the set C∖S to be finite, together with a procedure and computational tools to check whether such a set is finite and, if so, compute its elements. As a consequence of this result, we provide a characterization for an ideal I of an affine semigroup S so that S∖I is a finite set. If so, we provide some procedures to compute the set S∖I.

Keywords

• affine semigroup
• ideal of a semigroup
• C -semigroup%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm3011"> <mml:semantics> <mml:mi mathvariant="script">C</mml:mi> </mml:semantics> </mml:math></inline-formula></named-content>-semigroup
• generalized numerical semigroup