In this paper, we have introduced the notion of vague Lie ideal and have studied their related properties. The cartesian products of vague Lie ideals are discussed. In particular, the Lie homomorphisms between the vague Lie ideals of a Lie algebra and the relationship between the domains and the co-domains of the vague Lie ideals under these Lie homomorphisms are investigated. Mathematics subje...

In a previous paper (see Garsia-Reutenauer [2]), we have studied algebraic properties of the descent algebras Σ n , and shown how these are related to the canonical decomposition of the free Lie algebra corresponding to a version of Poincaré-Birkhoff-Witt's theorem. In the present paper, we study homomorphisms between these algebras Σ n. The existence of these homomorphisms was suggested by pro...

We prove a q-analogue of the row and column removal theorems for homomorphisms between Specht modules proved by Fayers and the first author [16]. These results can be considered as complements to James and Donkin’s row and column removal theorems for decomposition numbers of the symmetric and general linear groups. In this paper we consider homomorphisms between the Specht modules of the Hecke ...

These notes are an introduction to basic properties of AndréQuillen homology for commutative algebras. They are an expanded version of my lectures at the summer school: Interactions between homotopy theory and algebra, University of Chicago, 26th July 6th August, 2004. The aim is to give fairly complete proofs of characterizations of smooth homomorphisms and of locally complete intersection hom...

In this paper, some properties of the dual B-homomorphism are provided, along with natural and fundamental theorem B-homomorphisms for B-algebras. The first third isomorphism theorems B algebra also presented in paper.

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal...

data types (ADT's) ADT's specify the theory of a signature algebra as a system of equations. Typically, these equations refer to terms in particular datatypes and the algebraic theory is executable by a rewrite semantics. An executable algebraic theory combines speci cation with the design of an implementation. The external view of an ADT hides both its implementation and its theory, revealing ...

We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product A ⊗h A labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Mori...

The articles [22], [25], [26], [28], [8], [9], [11], [21], [23], [3], [12], [10], [1], [19], [6], [27], [18], [15], [2], [5], [4], [16], [7], [24], [13], [14], [17], and [20] provide the notation and terminology for this paper. For simplicity we follow the rules: U1, U2, U3 denote universal algebras, n denotes a natural number, A denotes a non empty set, and h denotes a function from U1 into U2...