r-IDEAL IN A FRAME

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.

کلیدواژه ها:

Frame ، r-ideal ، minimal prime ideal ، Boolean algebra