A Special Class of Rings

Nagaiah, T.; Valluri, M. R.

doi:10.47836/mjms.16.1.11

MJMS

2022

DOI: 10.47836/mjms.16.1.11

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A Special Class of Rings

T. Nagaiah¹,

M. R. Valluri²

Abstract: In this paper, a special class of rings for which an element a in R, satisfying the additional property an=an−1+an−1, for an integer n>1 is introduced and several results and examples related to this special class of rings is presented.

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2024

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Cited by 2 publications

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The Squared-Zero Product Probability of Some Ring of Matrices over Integers Modulo Prime

Zaid,

Sarmin,

Khasraw

2024

MJMS

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Recently, the study of probabilities in ring theory has shown a significant increase in the field of algebra. Many interesting algebraic structures were modeled to find their probabilities in certain finite rings. In this paper, we introduce a new type of probability in finite rings, namely the squared-zero product probability. The aim is to study the square property and the zero product property of the ring. The focus of this study is the ring of matrices of dimension two over integers modulo prime p. To obtain the probability, the order of the square-annihilator of the ring is determined. The results found show that the squared-zero product probability of the ring is dependent on the value of p.

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The Squared-Zero Product Probability of Some Ring of Matrices over Integers Modulo Prime

Zaid,

Sarmin,

Khasraw

2024

MJMS

View full text Add to dashboard Cite

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On the Relation Between Topological Free and Topological Dual Injective Modules

Alkhayyat,

Mahameed,

Salih

2024

MJMS

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Algebraic topology is a branch of mathematics which use the concepts of abstract algebra to study topological spaces in which to find algebraic invariants that classify topological spaces up to homeomorphism. In this paper, the basic properties of some concepts on algebraic topology such as the topological ring, the topological module, and the topological free module were recalled, which were helped to define new concepts and proof some of there properties as a new results. Then, some results related to the relation between the free topological module and homomorphism topology. As in any application will be introduced, the tensor concept will be chosen to explain the new results related to the topological module.

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A Special Class of Rings

Abstract: In this paper, a special class of rings for which an element a in R, satisfying the additional property an=an−1+an−1, for an integer n>1 is introduced and several results and examples related to this special class of rings is presented.

Cited by 2 publications

References 4 publications

The Squared-Zero Product Probability of Some Ring of Matrices over Integers Modulo Prime

The Squared-Zero Product Probability of Some Ring of Matrices over Integers Modulo Prime

On the Relation Between Topological Free and Topological Dual Injective Modules

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