Prime ideals and spectral topological conditions on hoops

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Payame Noor University, P. O. Box 19395-4697, Tehran, Iran.

2 Computer Engineering Department, Velayat University, Iranshahar, Iran. Chabahar Maritime University, Chabahar, Iran.

Abstract

This paper delves into the investigation of ideals and prime ideals within hoops, a distinct class of algebraic structures. It seeks to identify and analyze specific properties of prime ideals, which are essential for comprehending the behavior of hoops. The notion of a local hoop is introduced, accompanied by an examination of its various equivalent definitions, showcasing its importance within the broader framework of hoop theory. A notable result presented is the proof that if a maximal ideal, denoted as $M$, exists in a hoop, the resulting quotient structure is locally finite, shedding light on the constraints and characteristics of these ideals. Furthermore, the paper introduces a topology on the set of all prime ideals associated with a hoop and explores the conditions required for this topology to be Hausdorff, offering new insights into the topological organization of prime ideals.

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References

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Algebraic Structures and Their Applications

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Available Online from 25 April 2026

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