When every finitely presented proper ideal is regular

Jawad Squalli

doi:10.56947/gjom.v7i2.189

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When every finitely presented proper ideal is regular

Jawad Squalli

Year: 2019 Journal: Gulf Journal of Mathematics Vol: 7 (2)

DOI: 10.56947/gjom.v7i2.189

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Abstract

In this paper we introduce and investigate a class of those rings in which every finitely presented proper ideal is regular. We establish the transfer of this notion to the trivial ring extension, direct product and homomorphic image, and then generate new and original families of rings satisfying this property.

Keywords:

Ideal (ethics) Homomorphic encryption Mathematics Finitely-generated abelian group Class (philosophy) Property (philosophy) Extension (predicate logic) Pure mathematics Ring (chemistry) Stallings theorem about ends of groups Transfer (computing) Product (mathematics) Image (mathematics) Direct product Discrete mathematics Algebra over a field Computer science Programming language Law Artificial intelligence Geometry

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Rings, Modules, and Algebras

Physical Sciences → Mathematics → Algebra and Number Theory

Commutative Algebra and Its Applications

Physical Sciences → Mathematics → Algebra and Number Theory

Advanced Algebra and Logic

Physical Sciences → Computer Science → Computational Theory and Mathematics

When every finitely presented proper ideal is regular

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