We propose a generalization of a conjecture of D. Quillen, on the vanishing of André-Quillen homology, to simplicial commutative rings. This conjecture characterizes a notion of local complete intersection, extended to the simplicial setting, under a suitable hypothesis on the local characteristic. Further, under the condition of finite-type homology, we then prove the conjecture in the case of...

The study of m-primary irreducible ideals in a commutative graded connected Noetherean algebra over a field is in principal equivalent to the study of the corresponding quotient algebras. Such algebras are Poincaré duality algebras. The prototype of such an algebra (apart from the cosmetic difference of being graded commutative rather than commutative graded) is the cohomology with field coeffi...

We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general construction based on graphs, and its non-commutative dual is realized in three different ways, in particular as the Grossman-Larson algebra of heap ordered trees....

In this paper, we determine the character space of vector-valued Lipschitz algebra Lipd(X, E), where (X, d) is any metric and E a certain unital semisimple commutative *-Banach algebra.

The aim of this paper is to study the properties of dual BCK-algebra and to prove that the MV -algebra is equvalent to the bounded commutative dual BCK-algebra.

in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...

I show that simple finite vertex algebras are commutative, and that the Lie conformal algebra structure underlying a reduced (= without nilpotent elements) finite vertex algebra is nilpotent.

The commutative algebra of all canonical affinor structures on homogeneous k-symmetric spaces is completely described. It gives a classification of these spaces with respect to the algebra.

We discuss two versions of a conjecture attributed to M Barr The Harrison cohomology of a commutative algebra is known to coincide with the Andr e Quillen cohomology over a eld of characteristic zero but not in prime characteristics The conjecture is that a modi ed version of Harrison cohomology taking into account torsion always agrees with Andr e Quillen cohomology We give a counterexample De...