We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following Malvenuto and Reutenauer, we pass from symmetric functions to non-commutative symmetric functions and from there to the algebra of permutations in order to relate...

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...

0. Introduction. This paper continues the study of the noncommutative innn-itesimal cohomology we introduced in 3]. This is the cohomology of sheaves on a noncommutative version of the commutative innnitesimal site of Grothendieck ((8]). Grothendieck showed that, for a smooth scheme X of characteristic zero, the cohomology of the structure sheaf on the innnitesimal site gives de Rham cohomol-og...

In [15], Kaplansky introduced Baer rings as rings in which every right (left) annihilator ideal is generated by an idempotent. According to Clark [9], a ring R is called quasi-Baer if the right annihilator of every right ideal is generated (as a right ideal) by an idempotent. Further works on quasi-Baer rings appear in [4, 6, 17]. Recently, Birkenmeier et al. [8] called a ring R to be a right (...

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...

First order theories for which the truth of a universal sentence on their finite models implies the truth on all models are investigated. It is proved that an equational theory has such a property if and only if every finitely presented model is residually finite. The most common classes of algebraic structures are discussed. 0. Introduction. John T. Baldwin in a review of the book Selected pap...

For a partition $$\varvec{k} = (k_1, \dots , k_m)$$ of n consider the group $$\mathrm {U}(\varvec{k}) \mathrm {U}(k_1) \times {U}(k_m)$$ block diagonally embedded in {U}(n)$$ and center $$\mathbb {T}^m$$ {U}(\varvec{k})$$ . We study Toeplitz operators with -invariant symbols acting on weighted Bergman spaces unit ball {B}^n$$ introduce $$(\varvec{k},j)$$ -quasi-radial quasi-homogeneous as those...

We introduce the notion of a graded integral element, prove the counterpart of the lying-over theorem on commutative algebra in the context of left commutative rngs, and use the Hu-Liu product to select a class of noncommutative rings. Left commutative rngs were introduced in [1]. I have two reasons to be interested in left commutative rngs. The first reason is that left commutative rngs are a ...

Shuffles have a long history, starting with the probabilistic study of card shufflings in the first part of the 20th century by Borel, Hadamard, Poincaré and others. Their theory was revived in the 50’s, for various reasons. In topology, the combinatorics of (non commutative) shuffle products was the key to the definition of topological products such as the ones existing on cochain algebras and...