DM-GAA

Article in press

Authors:

A Goswami

Amartya Goswami

University of Johannesburg

email: agoswami@uj.ac.za

Title:

Primitive ideals and Jacobson's structure spaces of semigroups

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Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2023-11-28 , Revised: 2024-04-04 , Accepted: 2024-04-05 , Available online: 2025-01-20 , https://doi.org/10.7151/dmgaa.1469

Abstract:

The purpose of this note is to introduce primitive ideals of semigroups and study some topological aspects of the corresponding structure spaces. We show that every structure space of a semigroup is $T_0$, quasi-compact, and every nonempty irreducible closed subset has a unique generic point. Moreover, such a structure space is Hausdorff if and only if every primitive ideal of the semirgroup is minimal. Finally, we define continuous maps between structure spaces of semigroups.

Keywords:

semigroup; primitive ideal; Jacobson topology

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