Formal power series rings with one absorbing factorization
Sana Hizem
Department of Mathematics, Faculty of Sciences, University of Monastir, Tunisia
Pages 132-138 | Received 01 December 2021, Accepted 05 February 2022, Published 01 June 2022
Abstract
Let R be a commutative ring with identity. A proper ideal I of R is said to be 1-absorbing prime ideal if whenever xyz \in I for some nonunit elements x,y,z\in R, then either xy\in I or z\in I. The ring R is called a 1-absorbing prime factorization ring (OAF-ring) if every proper ideal has an OA-factorization. In this note, we characterize commutative rings R (respectively, ring extensions A\subset B) for which the ring of formal power series R[[X]] (respectively, the ring A+XB[X] or A+XB[[X]]) is an OAF-ring.
Keywords: OA-ideals, OAF-rings, formal power series rings.
MSC numbers: 13A15, 13B25, 3F25, 13F15, 13B99.
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