Congruences in seminearrings and their correspondence with strong ideals

Document Type : Research Paper

Authors

Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India.

Abstract

In this paper, we define the notion of strong ideal of a seminearring $S.$ If $S$ is a nearring or a ring then the concept of a strong ideal of $S$ coincides with the usual ideal of $S.$ We show that there is one-one correspondence between strong ideals of $S$ and strong congruences on $S$. Using the concept of strong ideals, we prove classical isomorphism theorems on $S$. We study insertion of factors property and obtain basic results on equisemiprime ideals.

Keywords

References

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Algebraic Structures and Their Applications

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Available Online from 01 February 2024

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