A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

After recalling briefly the main properties of the amalgamated duplication of a ring R along an ideal I , denoted by R1 I [5], we restrict our attention to the study of the properties of R1 I , when I is a multiplicative canonical ideal of R [9]. In particular, we study when every regular fractional ideal of R1I is divisorial.

In this paper, we introduce the new concept of biprojectivity of a Banach algebra modulo an ideal, as a generalization of this notion in the classical case. By using it , we obtain some necessary and sufficient conditions for contractibility of Banach algebras modulo an ideal. In particular we characterize the contractibility of quotient Banach algebras. Also we study the relationship between t...

in this paper we investigate some hereditary properties of amenability modulo an ideal of banach algebras. we show that if (e) is a bounded approximate identity modulo i of a banach algebra a and x is a neo-unital modulo i, then (e) is a bounded approximate identity for x. moreover we show that amenability modulo an ideal of a banach algebra a can be only considered by the neo-unital modulo...

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...

Let R be a commutative ring with identity and let I be an ideal of R. Let R 1 I be the subring of R×R consisting of the elements (r,r + i) for r ∈ R and i ∈ I. We study the diameter and girth of the zero-divisor graph of the ring R 1 I.