Shahrood University of TechnologyJournal of Algebraic Systems2345-5128Articles in Press20240918r-ideal in a frame325810.22044/jas.2024.14192.1806ENAli Akbar EstajiHakim Sabzevari University0000-0001-8993-5109Rahimeh PourkhandaniFaculty of Mathematics and Computer Sciences
Hakim Sabzevari University
Sabzevar
IranZohreh Norozi KhoshmardanFaculty of Mathematics and Computer Sciences
Hakim Sabzevari University
Sabzevar
IranJournal Article20240214Recently, 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.