r-ideal in a frame

Articles in Press

Document Type : Original Manuscript

Authors

1 Hakim Sabzevari University

2 Faculty of Mathematics and Computer Sciences Hakim Sabzevari University Sabzevar Iran

10.22044/jas.2024.14192.1806

Abstract

Recently, the concept of r-ideal was introduced in a commutative ring and also in a commutative semigroup. Here, we provide a similar definition for r-ideal in a frame and investigate some
of its properties. Some cases confirm that the properties of r-ideal in frames do not coincide with properties of r-ideal in commutative rings (or in commutative semigroups), necessarily. We find some characterization of r-ideal in a frame. Specially, we show that any proper r-ideal in a frame is an intersection of minimal prime ideals in this frame. Also, we establish a condition in which each ideal in a frame is an r-ideal as a characterization for boolean algebras.

Keywords

Journal of Algebraic Systems

Articles in Press, Accepted Manuscript
Available Online from 18 September 2024

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