Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 1 2026 01 01 r-IDEAL IN A FRAME 157 172 3258 10.22044/jas.2024.14192.1806 EN Ali Akbar Estaji Faculty of Mathematics and Computer Science, Hakim Sabzevari University, Sabzevar, Iran. Rahimeh Pourkhandani Faculty of Mathematics and Computer Science, Hakim Sabzevari University, Sabzevar, Iran. Zohreh Norozi Khoshmardan Faculty of Mathematics and Computer Science, Hakim Sabzevari University, Sabzevar, Iran. Journal Article 2024 02 14 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<br />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. https://jas.shahroodut.ac.ir/article_3258_efd7b3b37b6ccb8d86c8ce88d2ffd717.pdf