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.
Estaji, A. A., Pourkhandani, R., & Norozi Khoshmardan, Z. (2024). r-ideal in a frame. Journal of Algebraic Systems, (), -. doi: 10.22044/jas.2024.14192.1806
MLA
Ali Akbar Estaji; Rahimeh Pourkhandani; Zohreh Norozi Khoshmardan. "r-ideal in a frame", Journal of Algebraic Systems, , , 2024, -. doi: 10.22044/jas.2024.14192.1806
HARVARD
Estaji, A. A., Pourkhandani, R., Norozi Khoshmardan, Z. (2024). 'r-ideal in a frame', Journal of Algebraic Systems, (), pp. -. doi: 10.22044/jas.2024.14192.1806
VANCOUVER
Estaji, A. A., Pourkhandani, R., Norozi Khoshmardan, Z. r-ideal in a frame. Journal of Algebraic Systems, 2024; (): -. doi: 10.22044/jas.2024.14192.1806