On Subsemigroups of Finitely Presented Semigroups
نویسندگان
چکیده
The purpose of this paper is to investigate properties of subsemigroups of finitely presented semigroups, particularly with respect to the property of being finitely presented. More precisely, we will consider various instances of the following: Main Problem. Let S be a finitely presented semigroup. Ž . Ž . i Is every subsemigroup ideal, one-sided ideal of S finitely generated? Ž . Ž . ii Is every subsemigroup ideal, one-sided ideal of S which is finitely generated as a semigroup finitely presented? Ž . Ž . iii Is every subsemigroup ideal, one-sided ideal of finite index in S Ž . finitely presented? For the definition of index see below. For example, if S is finite all these questions have an affirmative answer. Ž . Less trivially, if S is a commutative semigroup then ii has an affirmative w x w x answer; see 12 . Also, in 2 it has been proved that a two-sided ideal of finite index in a finitely presented semigroup is always finitely presented.
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