PRIMITIVE IDEALS AND JACOBSON’S STRUCTURE SPACES OF SEMIGROUPS

Amartya Goswami

doi:10.7151/dmgaa.1469

PRIMITIVE IDEALS AND JACOBSON’S STRUCTURE SPACES OF SEMIGROUPS

Amartya Goswami

Mathematics and Applied Mathematics

National Institute for Theoretical and Computational Sciences (NITheCS)

Research output: Contribution to journal › Article › peer-review

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 T₀, 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.

Original language	English
Pages (from-to)	125-134
Number of pages	10
Journal	Discussiones Mathematicae - General Algebra and Applications
Volume	45
Issue number	1
DOIs	https://doi.org/10.7151/dmgaa.1469
Publication status	Published - 2025

Keywords

Jacobson topology
primitive ideal
semigroup

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.7151/dmgaa.1469

Cite this

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PRIMITIVE IDEALS AND JACOBSON’S STRUCTURE SPACES OF SEMIGROUPS

Abstract

Keywords

ASJC Scopus subject areas

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