Let R be a commutative ring, V a nitely generated free R-module and G leGL R (V) a nite group acting naturally on the graded symmetric algebra A = S(V). Let (V; G) denote the minimal number m, such that the ring A G of inva riants can be generated by nitely many elements of degree at most m. For G = n and V (n; k), the k-fold direct sum of the natural permutat ion module, one knows that (V (n; ...

A graphG = (V,E) is called a chordal ring and denoted by CR(N, d), if V = {0, 1, · · · , N− 1} and E = {(u, v) | [v − u]N = 1 or [v − u]N = d, 2 ≦ d ≦ N/2)}, where [v − u]N denotes v − u modulo N . A graph G = (V,E) is called an extended chordal ring and denoted by CR(N, d1, d2), if V = {0, 1, · · · , N − 1} and E = {(u, v) | [v − u]N = 1 or [v − u]N = di, 1 ≦ i ≦ 2, 2 ≦ di ≦ N/2)}. CR(N, d1, N...

1. Basics Let A = fa 1 ; : : :; a n g be a subset of N d n f0g, A be the matrix with columns a i , and suppose that rank(A) = d. Consider the polynomial ring S = kx 1 x i 7 ! t a i = t a i1 1 : : : t a id d is called a toric ideal. For an integer vector v = (v 1 ; : : :; v n) we set x v = x v 1 1 : : : x v n n. In this notation, the map ' acts as x v 7 ! t Av : Deenition 1.1. The toric ring is ...

Let $nin mathbb{N}$. An additive map $h:Ato B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $ain A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebras is norm continuous.

Let G be a finite simple graph on the vertex set $$V(G) = \{x_{1}, \ldots , x_{n}\}$$ and match(G), min-match(G) ind-match(G) matching number, minimum number induced of G, respectively. $$K[V(G)] K[x_{1}, x_{n}]$$ denote polynomial ring over field K $$I(G) \subset K[V(G)]$$ edge ideal G. The relationship between these graph-theoretic invariants ring-theoretic quotient K[V(G)]/I(G) has been stud...

A ring $R$ with an automorphism $sigma$ and a $sigma$-derivation $delta$ is called $delta$-quasi-Baer (resp., $sigma$-invariant quasi-Baer) if the right annihilator of every $delta$-ideal (resp., $sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let $A=sigma(R)leftlangle x...

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

Let V be an n-dimensional left vector space over a division ring R. We write Gk(V ) for the Grassmannian formed by k-dimensional subspaces of V and denote by Γk(V ) the associated Grassmann graph. Let also V ′ be an n′-dimensional left vector space over a division ring R′. Isometric embeddings of Γk(V ) in Γk′ (V ′) are classified in [13]. A classification of J(n, k)-subsets in Gk′ (V ′), i.e. ...

let d be a division ring with centre k and dim, d< ? a valuation on k and v a noninvariant extension of ? to d. we define the initial ramfication index of v over ?, ?(v/ ?) .let a be a valuation ring of o with maximal ideal m, and v , v ,…, v noninvariant extensions of w to d with valuation rings a , a ,…, a . if b= a , it is shown that the following conditions are equivalent: (i) b is a finite...

We give necessary and sufficient conditions for a skew polynomial ring K[t; σ, δ] over a division ring K to be a left V -domain. In particular, when this ring admits a unique simple left module, the conditions obtained include: 1) all polynomials are Wedderburn, 2) all n× n matrices over K are (σ, δ)-similar. We also provide necessary and sufficient conditions for this ring to be both left and ...