Extension of star-operation
Elmakki Ahmed\,^1 and Taha Eddhay\,^2
^1\,Department of Mathematics, Faculty of Sciences, Monastir, Tunisia.
^2\,Preparatory Institute for Engineering Studies, Gafsa, Tunisia.
Pages 36-44 | Received 19 June 2023, Accepted 22 September 2023, Published 30 June 2024
Abstract
Let D be an integral domain, * a star operation on D and S a multiplicative subset of D. In this paper, we generalize the notion of *-ideals (resp, *-invertible) of D, by introducing the concept of S–*-ideals (resp, S–*-invertible) of D. A fractional ideal of D is called S–*-ideals (resp, S–*-invertible) if there exists an s\in S such that sI^*\subseteq I\subseteq I^* (resp, if there exists an s\in S and a fractional ideal J of D such that sD \subseteq (IJ)^* \subseteq D). We investigate many proprieties and characterizations of the notion S–*-ideals (resp, S–*-invertible).
Keywords: *-operation, S–*-ideals, S–*-invertible.
MSC numbers: 13G05, 13A15
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