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Jung Won Cho

Publications and source records attributed to Jung Won Cho.

3 recordsLinked to original sources
arXiv2026

Howson property and finitely generated intersection problem for monogenic inverse semigroups

An algebraic structure is said to have the Howson property if the intersection of any two finitely generated subalgebras is finitely generated. We explore the Howson property in the context of monogenic inverse semigroups. It is known, due to work of Jones and Trotter (1989) and Jones (2016), that every monogenic inverse semigroup has the Howson property considered as an inverse semigroup, i.e. with respect to its inverse subsemigroups. In this paper, we consider monogenic inverse semigroups qua semigroups, i.e. we consider all their subsemigroups. We prove that every monogenic inverse semigroup possesses the Howson property in this broader sense, with the sole exception of the monogenic free inverse semigroup. For this exceptional case, we show that the problem of determining whether the intersection of two finitely generated subsemigroups is finitely generated is algorithmically decidable.

math.GR↗
arXiv2024

Generators and presentations of inverse subsemigroups of the monogenic free inverse semigroup

It was proved by Oliveira and Silva (2005) that every finitely generated inverse subsemigroup of the monogenic free inverse semigroup $FI_1$ is finitely presented. The present paper continues this development, and gives generating sets and presentations for general (i.e. not necessarily finitely generated) inverse subsemigroups of $FI_1$. For an inverse semigroup $S$ and an inverse subsemigroup $T$ of $S$, we say $S$ is finitely generated modulo $T$ if there is a finite set $A$ such that $S = \langle T, A \rangle$. Likewise, we say that $S$ is finitely presented modulo $T $ if $S$ can be defined by a presentation of the form $\text{Inv}\langle X, Y \mid R, Q\rangle$, where $\text{Inv}\langle X\mid R\rangle$ is a presentation for $T$ and $Y$ and $Q$ are finite. We show that every inverse subsemigroup $S$ of $FI_1$ is finitely generated modulo its semilattice of idempotents $E(S)$. By way of contrast, we show that when $S\neq E(S)$, it can never be finitely presented modulo $E(S)$. However, in the process we establish some nice (albeit infinite) presentations for $S$ modulo $E(S)$.

math.GR↗