Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGA-algebra) and X be a relatively free resolution of Λ over A. The standard bar resolution of Λ over A, denoted by B(A), provides an example of a resolution of this kind. The comparison theorem gives inductive formulae f :B(A) → X and g:X → B(A) termed comparison maps. In case that fg = 1X and A is connect...

Over a field IF of any characteristic, for a commutative associative algebra A with an identity element and for the polynomial algebra IF [D] of a commutative derivation subalgebra D of A, the associative and the Lie algebras of Weyl type on the same vector space A[D] = A ⊗ IF [D] are defined. It is proved that A[D], as a Lie algebra (modular its center) or as an associative algebra, is simple ...

In this paper we consider the algebra (A, f, g), where f and g are m-ary and n-ary operations on the set A. We define the concept of regular algebra and we prove that for a regular medial algebra (A, f, g) there exists a commutative semigroup (A,+) such that the operations f and g have linear representations on (A,+). As a corollary, we show that for a regular medial algebra (A,F ) there exists...

Louis Solomon showed that the group algebra of the symmetric group Sn has a subalgebra called the descent algebra, generated by sums of permutations with a given descent set. In fact, he showed that every Coxeter group has something which can be called a descent algebra. For any Coxeter group that is also a Weyl group, Paola Cellini proved the existence of a different, commutative subalgebra of...

let  be a banach algebra and  a derivation. in this paper, it is proved, under certain conditions, that , where  is the jacobson radical of . moreover, we prove that if  is unital and  is a continuous derivation, then , where  denotes the set of all primitive ideals such that  is commutative,  denotes the set of all maximal (modular) ideals such that  is commutative, and  is the set of all non-...

Often A is called H-module algebra. We refer reader to [11, 6] for the basic information concerning Hopf algebras and their actions on associative algebras. Definition 1.2 The invariants of H in A is the set AH of those a ∈ A, that ha = ε(h)a for each h ∈ H. Straightforward computations show, that AH is subalgebra of A. The notion of action of Hopf algebra on associative algebra generalize the ...

We develop results which show that elements in the radical of a commutative Banach algebra are often precluded from having prime-like properties if we avoid certain exceptional situations involving torsion elements. This makes the proof of the Singer-Wermer conjecture conceptually much clearer. It also motivates the de nition of an element having regular powers and allows us to strengthen our p...

Let A be a finitely generated commutative algebra over a field K with a presentation A = K〈X1, . . . , Xn | R〉, where R is a set of monomial relations in the generators X1, . . . , Xn. So A = K[S], the semigroup algebra of the monoid S = 〈X1, . . . , Xn | R〉. We characterize, purely in terms of the defining relations, when A is an integrally closed domain, provided R contains at most two relati...

The notion of fuzzy s-prime filters of a bounded BCK-algebra is introduced.We discuss the relation between fuzzy s-prime filters and fuzzy prime filters. By the fuzzy s-prime filters of a bounded commutative BCK-algebra X, we establish a fuzzy topological structure on X. We prove that the set of all fuzzy s-prime filters of a bounded commutative BCK-algebra forms a topological space. Moreover, ...