Implicative Ideal of a Pseudoring

Tadesse Nigisa  Natei; Kolluru  Venkateswarlu; Dawit Cherinet  kifetaw

doi:10.20372/au.jssd.14.1.2026.0714

Implicative Ideal of a Pseudoring

Authors

Tadesse Nigisa Natei Department of Mathematics, Arba Minch University, Ethiopia
Kolluru Venkateswarlu Department of Computer Science and Systems Engineering, Andhra University Visakhapatnam, Andhra Pradesh, Indi,
Dawit Cherinet kifetaw Department of Mathematics, Arba Minch University, Arba Minch, Ethiopia

DOI:

https://doi.org/10.20372/au.jssd.14.1.2026.0714

Keywords:

Finite product property, Implicative ideal of a pseudoring, Maximal ideal of a pseudoring, Prime ideal of a pseudoring

Abstract

In this study, we present the notion of an implicative ideal of a pseudoring and characterize it. We also introduce the notion of a finite product property of a subset of a pseudoring and prove its relations with the implicative and other types of ideal of a pseudoring. Moreover, we demonstrate the relationship between an implicative ideal with prime, polar ideals, as well as the atom of an atomic pseudoring. Finally, we prove that a prime ideal is implicative if and only if it is a maximal ideal of R.

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Published

2026-01-30

How to Cite

Natei, T. N. ., Venkateswarlu, K. ., & kifetaw, D. C. . (2026). Implicative Ideal of a Pseudoring. Journal of Science and Sustainable Development, 14(1), 75-83. https://doi.org/10.20372/au.jssd.14.1.2026.0714