In the present paper, by considering the notion of ideals in $MV$-algebras, we study some kinds of ideals in $MV$-algebras and obtain some results on them. For example, we present definition of ultra ideal in $MV$-algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in $MV$...

In this paper we have discussed the relations between Maximal ideal, Prime ideal and irreducible ideal in an incline R. Mathematics Subject Classification: 16D25, 16Y60

For a Banach space X, let B(X) denote the Banach algebra of all continuous linear operators on X. First, we study the lattice of closed ideals in B(Jp), where 1 < p < ∞ and Jp is the pth James space. Our main result is that the ideal of weakly compact operators is the unique maximal ideal in B(Jp). Applications of this result include the following. (i) The Brown–McCoy radical of B(X), which by ...

In this note, we study how the depths of multiplier ideals behave under restriction. We also study possible values of the depths of multiplier ideals in the filtrations induced from maximal ideal sheaves. We then use it to give a sufficient condition for the integral closedness of the product of a multiplier ideal and a power of maximal ideal sheaf in the spirit of Huneke.

The basic notion of the article is a pair (A, U), whereA is a commutative C-algebra and U is a partial isometry such thatA ∋ a → UaU is an endomorphism of A and UU ∈ A. We give a description of the maximal ideal space of the smallest coefficient C-algebra E∗(A) of the algebra C(A, U) generated by the system (A, U).

We prove that every maximal coonitary group has size at least the cardinality of the smallest non{meager set of reals. We also provide a consistency result saying that the spectrum of possible cardinalities of maximal coonitary groups may be quite arbitrary.

Let G denote a locally compact abelian topological group (an l.c.a. group) with dual group C\ We will denote by A7(G) the Banach algebra of bounded regular Borel measures on G under convolution multiplication and by L(G) the algebra of bounded measures absolutely continuous with respect to Haar measure on G (for discussions of these Banach algebras cf. [1], [2], and [5]). In this paper we shall...

We study the structure of the maximal ideal space M(H∞) of the algebra H ∞ = H∞(D) of bounded analytic functions defined on the open unit disk D ⊂ C. Based on the fact that dim M(H∞) = 2 we prove for H∞ the matrix-valued corona theorem. Our results heavily rely on the topological construction describing maximal ideal spaces of certain algebras of continuous functions defined on the covering spa...