Falling -Ideals in -Algebras

Frames in right ideals of $C^*$-algebras

we investigate the problem of the existence of a frame forright ideals of a C*-algebra A, without the use of the Kasparov stabilizationtheorem. We show that this property can not characterize A as a C*-algebraof compact operators.

Ultra and Involution Ideals in $BCK$-algebras

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...

Radical of $cdot$-ideals in $PMV$-algebras

‎In this paper‎, ‎we introduce the notion of the radical of a $PMV$-algebra $A$ and we charactrize radical $A$ via elements of $A$‎. ‎Also‎, ‎we introduce the notion of the radical of a $cdot$-ideal in $PMV$-algebras‎. ‎Several characterizations of this radical is given‎. ‎We define the notion of a semimaximal $cdot$-ideal in a $PMV$-algebra‎. ‎Finally we show that $A/I$ has no nilpotent elemen...

The Theory of Falling Shadows Applied to d-Ideals in d-Algebras

Falling Pseudo d-Ideals and d-Subalgebras in Pseudo d-Algebras

Based on the theory of a falling shadow which was first formulated by Wang [15], a theoretical approach of the pseudo ideal structure in pseudo d-algebras is established. Several properties are investigated, and relations among a falling pseudo d-subalgebra, a falling pseudo BCK-ideal and a falling pseudo d-ideal are discussed. A characterization of a falling pseudo d-ideal is provided. Conditi...