g(x)-p-Clean Rings

Document Type : Original Scientific Paper

Author

‎Department of‎ Basic Sciences, ‎Technical and Vocational University (TVU), Tehran‎, ‎Iran

10.22052/mir.2026.257202.1526

Abstract

‎Let $R$ be a unital additive ring‎, ‎C(R) denote the center of the ring R and g(x)  be a polynomial in‎
‎$ C(R)[x] $‎. ‎We explore a new ring structure called a g(x)-p-clean ring‎. ‎An element r is said to be g(x)-p-clean if it can be decomposed into r = p‎ + ‎s‎, ‎where p belongs to the set of pure elements Pu(R)‎, ‎and s is a root of the polynomial $ g(x) $‎. ‎This study examines the core properties of such rings‎. ‎We show‎, ‎for instance‎, ‎that if R admits the g(x)-p-clean property and I is an ideal of R‎, ‎then the quotient ring R/I also inherits this property provided $\overline{ g}(x)\in C(R/I)[x]$‎. ‎We establish a number of structural results concerning these rings‎.

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References

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Mathematics Interdisciplinary Research
Volume 11, Issue 2
In Progress
June 2026
Pages 177-184

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