Using a result from Herzog [2] we prove the following. Let (B0, n0) be an artinian local algebra of embedding dimension v over some field L with tangent cone gr(B0) ∼= L[X1, . . . , Xv]/I0. Suppose the ideal I0 is generated by power products of degree 2. Then for every residually rational flat local homomorphism (A,m) → (B, n) of local L-algebras that has a special fiber isomorphic to B0 the (v...

Given a finitely presented group G = 〈X;R〉, the word problem asks to decide effectively whether a given word in the free group w ∈ F (X) represents the identity element in G or not. Another important computational problem is to check effectively whether G is finite or not. For the ”No” parts of these problems, we can use quotient tests. For instance, for the ”No” part of the word problem, we ca...

Let KG be the group ring of a group G over a commutative ring K with unity. The rings KG are described for which xxσ = xσx for all x = ∑ g∈G αgg ∈ KG, where x → xσ = ∑ g∈G αgf(g)σ(g) is an involution of KG; here f : G → U(K) is a homomorphism and σ is an antiautomorphism of order two of G. Let R be a ring with unity. We denote by U(R) the group of units of R. A (bijective) map : R → R is called...

For any abelian Polish σ-compact group H there exist an Fσ ideal Z ⊆ P (N) and a Borel Z -approximate homomorphism f : H → HN which is not Z -approximable by a continuous true homomorphism g : H → HN .

let $r$ be a ring with unity. the undirected nilpotent graph of $r$, denoted by $gamma_n(r)$, is a graph with vertex set ~$z_n(r)^* = {0neq x in r | xy in n(r) for some y in r^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in n(r)$, or equivalently, $yx in n(r)$, where $n(r)$ denoted the nilpotent elements of $r$. recently, it has been proved that if $r$ is a left ar...

This paper concerns a relationship between soft sets and n-ary polygroups. We consider the notion of an n-ary polygroup as a generalization of a polygroup and apply the notion of soft sets to n-ary polygroups. Some related notions are defined and several basic properties are discussed by using the soft set theory. Furthermore, we propose the homomorphism of n-ary polygroups and investigate the ...

In this paper, we introduce the Harish-Chandra homomorphism for quantum superalgebra $$\mathrm {U}_q({\mathfrak {g}})$$ associated with a simple basic Lie $${\mathfrak {g}}$$ and give an explicit description of its image. We use it to prove that center is isomorphic subring ring $$J({\mathfrak exponential super-invariants in sense Sergeev Veselov, establishing type theorem . As byproduct, obtai...

The motivation for this work was a calculation by Oshanin of the image of the signature homomorphism from the special unitary cobordism ring into the integers. Here we compute this image for symplectic cobordism. This is accomplished by proving two divisibility theorems and then giving examples to show the theorems are the best possible.

A Lie algebra gQ over Q is said to be R-universal if every homomorphism from gQ to gl(n,R) is conjugate to a homomorphism into gl(n,Q) (for every n). By using Galois cohomology, we provide a short proof of the known fact that every real semisimple Lie algebra has an R-universal Q-form. We also provide a classification of the R-universal Lie algebras that are semisimple.

We show that a connected split reductive group G over a field of characteristic 0 is uniquely determined up to isomorphism by specifying a maximal torus T of G , the set of isomorphism classes of irreducible representations of G , and the character homomorphism from the Grothendieck ring of G to that of T .