Absorbing ideals of the form I[[X]]
Sana Hizem
Department of Mathematics, Faculty of Sciences, University of Monastir, Tunisia.
Pages 170-177 | Received 24 August 2023, Accepted 03 November 2023, Published 30 June 2024
Abstract
Let R be a commutative ring with identity and n a positive integer. In [1], Anderson and Badawi define a proper ideal I of a commutative ring R to be n-absorbing if whenever x_{1}\cdots x_{n+1}\in I for x_{1},…,x_{n+1}\in R, then there are n of the x_{i}^{\prime }s whose product is in I. In this paper we investigate the transfer of the property n-absorbing from the ideal I of R to the ideal I[[X]] of the formal power series ring R[[X]].
Keywords: absorbing ideals, strongly absorbing ideals, formal power series rings.
MSC numbers: Primary 13A15; 13F25; 13F05; Secondary 13A99.
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