In this paper, we introduce a strategy for studying simplicial commutative algebras over general commutative rings R. Given such a simplicial algebra A, this strategy involves replacing A with a connected simplicial commutative k(℘)-algebra A(℘), for each ℘ ∈ Spec(π0A), which we call the connected component of A at ℘. These components retain most of the André-Quillen homology of A when the coef...

We show that the multiplier algebra of the Fourier algebra on a locally compact group G can be isometrically represented on a direct sum on non-commutative L spaces associated to the right von Neumann algebra of G. If these spaces are given their canonical Operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful ...

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...

Hilbert algebras are important tools for certain investigations in algebraic logic since they can be considered as fragments of any propositional logic containing a logical connective implication and the constant 1 which is considered as the logical value “true”. The concept of Hilbert algebras was introduced in the 50-ties by L. Henkin and T. Skolem (under the name implicative models) for inve...

The quadratic algebras Qn are associated with pseudo-roots of noncommutative polynomials. We compute the Hilbert series of the algebras Qn and of the dual algebras Q ! n. Introduction Let P (x) = x−a1x n−1 + · · ·+(−1)an be a polynomial over a ring R. Two classical problems concern the polynomial P (x): nvestigation of the solutions of the equation P (x) = 0 and the decomposition of P (x) into ...

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 prove that every implicative aBE algebra satisfies the transitivity property. This means is a Tarski algebra, and thus also commutative BCK algebra.

At first, we recall the basic concept, By a residual lattice is meant an algebra ) 1 , 0 , , , , , ( o ∗ ∧ ∨ = L L such that (i) ) 1 , 0 , , , ( ∧ ∨ = L L is a bounded lattice, (ii) ) 1 , , ( ∗ = L L is a commutative monoid, (iii) it satisfies the so-called adjoin ness property: y z y x = ∗ ∨ ) ( if and only if y x z y o ≤ ≤ Let us note [7] that y x ∨ is the greatest element of the set y z y x ...

In this paper, we acquaint new kinds of ideals BCK-algebras built on tripolar picture fuzzy structures. fact, the notions ideal, implicative ideal (commutative ideal) BCK-algebra are introduced, and related properties studied. Also, a relation among is well-known. Furthermore, it shown that may be but converse not correct in common. Further, obtained an BCK-algebra, aforementioned statement tru...