in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

In this paper we exhibit some examples of non-Gorenstein Hecke algebras, and hence some modular forms for which mod 2 multiplicity one does not hold. Define S2(Γ0(N)) to be the space of classical cuspidal modular forms of weight 2, level N , and trivial character. The Hecke algebra TN is defined to be the subring of End(S2(Γ0(N)) generated by the Hecke operators {Tp : p 6 |N} and {Uq : q|N}. Le...

The irreducible representations of the double cover of SL(m) with infinitesmal character 1p having a maximal primitive ideal are determined. We investigate whether these representations are attached to a nilpotent orbit and use the orbit method to speculate their K types. We conclude with a character formula expressing the representations as a sum of simpler virtual representions. Thesis Superv...

For the quaternion division algebra D over a non-Archimedean local field k, and π an irreducible finite dimensional representation of D×, say with trivial central character, we prove the existence of a quadratic extension K of k such that the trivial character of K× appears in π, as well as the existence of a quadratic extension L of k such that the trivial character of L× does not appear in π....

In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal m...

We study the representation theory of non-admissible simple affine vertex algebra [Formula: see text]. determine an explicit formula for singular vector conformal weight four in universal text], and show that it generates maximal ideal classify irreducible text]-modules category fusion rules between modules ordinary It turns out this is isomorphic to also prove text] a semi-simple, rigid braide...

In this paper a full categorization of irreducible classical Goppa codes of degree 4 and length 9 is given. It is an interesting example in the context of find the number of permutation non-equivalent classical irreducible maximal Goppa codes having fixed parameters q, n and r using group theory techniques.