%0 Journal Article
%T r-ideal in a frame
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Estaji, Ali Akbar
%A Pourkhandani, Rahimeh
%A Norozi Khoshmardan, Zohreh
%D 2024
%\ 09/18/2024
%V
%N
%P -
%! r-ideal in a frame
%K Frame
%K r-ideal
%K minimal prime ideal
%K Boolean algebra
%R 10.22044/jas.2024.14192.1806
%X 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 someof 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.
%U