String theories with two dimensional space-time target spaces are characterized by the existence of a “ground ring” of operators of spin (0, 0). By understanding this ring, one can understand the symmetries of the theory and illuminate the relation of the critical string theory to matrix models. The symmetry groups that arise are, roughly, the area preserving diffeomorphisms of a two dimensiona...

the concept of fuzzy soft γ-ring is introduced; and some properties of fuzzy soft γ-rings are given. then the definitions of fuzzy soft γ-ideals are proposed and some of their theories are considered.

The proposed embedded strain sensor consists of six elastic rings, placed in an icosahedral symmetry, whose measured elongations give access to the complete 3D tensor surrounding matrix. linear relationship between ring and matrix is given. From this relation it deduced that isotropic, i.e. its sensitivity independent rotation more sensitive hydrostatic strains than deviatoric strains. addition...

This work formally introduces and starts investigating the structure of matrix polynomial algebra extensions a coefficient by (elementary) matrix-variables over ground ring in not necessary commuting variables. These subalgebras full rings show up noncommutative algebraic geometry. We carefully study their (one-sided or bilateral) noetherianity, obtaining precise lift Hilbert Basis Theorem when...

Matrix-rings play a fundamental role in mathematics and its applications. A difficult question is to decide whether a given ring is isomorphic to a matrixring or one of its variants. Several “hidden matrix-rings” have been shown in the literature (see [5]). These rings did not appear as being matrix-rings at the first sight, nevertheless they proved out to be isomorphic to matrix-rings. Another...

Given an n×n matrix c over a unitary ring R, the centralizer of in full Mn(R) is called principal ring, denoted by Sn(c,R). We investigate its structure and prove: (1) If invertible with c-free point, or if R has no zero-divisors Jordan-similar all eigenvalues center then separable Frobenius extension Sn(c,R) sense Kasch. (2) integral domain matrix, cellular R-algebra Graham Lehrer. In particul...

We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic codes are ideals in the group ring over a cyclic group. The fresh focus is on the encodings themselves, which only under very limited conditions result in idea...

Both flash vacuum thermolysis (FVT) and matrix photolysis generate 2-diazomethylpyrazine (22) from 1,2,3-triazolo[1,5-a]pyrazine (24). FVT of 4-azidopyridine (18) as well as of 24 or 2-(5-tetrazolyl)pyrazine (23) affords the products expected from the nitrene, i.e., 4,4'-azopyridine and 2- and 3-cyanopyrroles. Matrix photolyses of both 18 and 24 result in ring expansion of 4-pyridylnitrene/2-py...

The classes of clean and nil-clean rings are closed with respect standard constructions as direct products and (triangular) matrix rings, cf. [12] resp. [4], while the classes of weakly (nil-)clean rings are not closed under these constructions. Moreover, while all matrix rings over fields are clean, [12] when we consider nil-clean rings there are strongly restrictions: if a matrix ring over a ...

In this paper, we propose a necessary and sufficient condition for the solvability to system of matrix equations over commutative quaternion ring, establish an expression its general solution when it is solvable. We also present algorithm finding approximate inconsistent. Finally, give example illustrate main results paper.