University of Kashan Mathematics Interdisciplinary Research 2538-3639 11 2 2026 06 01 g(x)-p-Clean Rings 177 184 115537 10.22052/mir.2026.257202.1526 EN Fatemeh Rashedi ‎Department of‎ Basic Sciences, ‎Technical and Vocational University (TVU), Tehran‎, ‎Iran Journal Article 2025 07 15 ‎Let $R$ be a unital additive ring‎, ‎C(R) denote the center of the ring R and g(x)  be a polynomial in‎<br />‎$ 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. https://mir.kashanu.ac.ir/article_115537_9ba44fa70ddf41ac4563631b013b1686.pdf