The standard reduced bar complex B(A) of a differential graded algebra A inherits a natural commutative algebra structure if A is a commutative algebra. We address an extension of this construction in the context of E-infinity algebras. We prove that the bar complex of any E-infinity algebra can be equipped with the structure of an E-infinity algebra so that the bar construction defines a funct...

The derived category of a general complete intersection of four quadrics in P has a semi-orthogonal decomposition 〈O(−2n + 9), . . . ,O(−1),O,D〉, where D is the derived category of twisted sheaves on a certain non-algebraic complex 3-fold coming from a moduli problem. In particular, when n = 4 we obtain a (twisted) derived equivalence of Calabi-Yau 3-folds predicted by Gross. This differs from ...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

A ring R is said to be semi-commutative if whenever a, b ∈ such that ab = 0, then aRb 0. In this article, we introduce the concepts of g−semi-commutative rings and g−N−semi-commutative several results concerning these two concepts. Let a G-graded g supp(R, G). Then with aRgb Also, − N−semi-commutative for any N(R) ⋂ Ann(a), bRg ⊆ Ann(a). We an example which N-semi-commutative some G) but itself...

Let $R$ be a non-commutative ring with unity. The commuting graph of $R$ denoted by $Gamma(R)$, is a graph with vertex set $RZ(R)$ and two vertices $a$ and $b$ are adjacent iff $ab=ba$. In this paper, we consider the commuting graph of non-commutative rings of order pq and $p^2q$ with Z(R) = 0 and non-commutative rings with unity of order $p^3q$. It is proved that $C_R(a)$ is a commutative ring...

The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative A-polynomial of twist knots. Our multivariable creative telescoping method allows us to compute linear recursions for sums of the form J(n) = P k c(n, k)Ĵ(k) given a recursion relation for (Ĵ(n)) a the hyp...

Reasoning about algebraic data types and functions that operate over these data types is an important problem for a large variety of applications. In this paper, we present a decision procedure for reasoning about data types using abstractions that are provided by catamorphisms: fold functions that map instances of algebraic data types into values in a decidable domain. We show that the procedu...