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 i...

• Let R be a ring. Let u ∈ N and v ∈ N, and let ai,j be an element of R for every (i, j) ∈ {1, 2, ..., u} × {1, 2, ..., v} . Then, we denote by (ai,j) 1≤i≤u the u× v matrix A ∈ Ru×v whose entry in row i and column j is ai,j for every (i, j) ∈ {1, 2, ..., u} × {1, 2, ..., v} . • Let R be a commutative ring with unity. Let P ∈ R [X] be a polynomial. Let j ∈ N. Then, we denote by coeffj P the coef...

Abstract Let R be a finite commutative ring. We define co-unit graph, associated to ring , denoted by G nu ( ) with vertex set V )) = U ), where is the of units and two distinct vertices x y being adjacent if only + ∉ / ). In this paper, we investigate some basic properties integers modulo n, for different values n. find domination number, clique number girth

The title oxovanadium(V) complex, [V(C(18)H(13)N(3)O(2))(CH(3)O)O(CH(3)OH)], was obtained by the reaction of 1-(2-hy-droxy-naphthalen-1-yl)ethanone, nicotinohydrazide and vanadyl sulfate in methanol. The V(V) atom is six-coordinated by the N,N,O-tridentate Schiff base ligand, one methano-late O atom, one methanol O atom and one oxide O atom, forming a distorted octa-hedral geometry. The methano...

 prsnt img-s rnring tht llows r viwpoint wlkthroughs o urn sns using just  w photogrphs s input. Commril pplitions suh s Googl trtviw, Bing ps t. us ruimntry orms o img-s rnring or urn visuliztion; mor sophistit pprohs us th ull D mol o th sn s input. As th qulity o Dmol grs, rnring rtits r...

We study the empirical measure L A n of the eigenvalues of non-normal square matrices of the form A n = U n D n V n with U n ,V n independent Haar distributed on the unitary group and D n real diagonal. We show that when the empirical measure of the eigenvalues of D n converges, and D n satisfies some technical conditions, L A n converges towards a rotationally invariant measure on the complex ...

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ = ( T M D 0 U N 0 0 V )

Borazine (B3N3H6) is known as ‘inorganic benzene’ because of a planar B3N3 ring with equivalent B-N distance. The lone pair from N in the ring delocalize to the adjacent p-orbital of B which leads to a conjugated system. Even though metal-benzene complexes have been studied extensively as models for cationπ interactions and organometallic bonding, similar systems with borazine is relatively sca...

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

This paper contains two essentially independent results in the invariant theory of finite groups. First we prove that, for any faithful representation of a non-trivial p-group over a field of characteristic p, the ring of vector invariants of m copies of that representation is not Cohen-Macaulay for m ≥ 3. In the second section of the paper we use Poincaré series methods to produce upper bounds...