The Grothendieckand Wittring of orthogonal representations of a finite group is defined and studied. The main application (only indicated) is the reduction of the computation of Wall's various L-groups for a finite group n to those subgroups of n, which are a semidirect product of a cyclic group y of odd order with a 2-group /?, such that any element in ft acts on y either by the identity or by...

In 1954 Zelinsky [16] proved that every element in the ring of linear transformations of a vector space V over a division ring D is a sum of two units unless dim V = 1 and D = Z2. Because EndD(V ) is a (von-Neumann) regular ring, Zelinsky’s result generated quite a bit of interest in regular rings that have the property that every element is a sum of (two) units. Clearly, a ring R, having Z2 as...

The title compound, C(15)H(12)N(2)OS, adopts a twisted V-shape, with the S atom as the pivot. The benzimidazole ring system [maximum deviation = 0.015 (1) Å] makes a dihedral angle of 78.56 (7)° with the phenyl ring. The O atom of the ketone group is close to coplanar with its adjacent ring [O-C-C-C torsion angle = 11.0 (2)°]. In the crystal, mol-ecules are linked by N-H⋯N hydrogen bonds into a...

Let $R$ be a unitary ring with an endomorphism $σ$ and $F∪{0}$ be the free monoid generated by $U={u_1,…,u_t}$ with $0$ added, and $M$ be a factor of $F$ setting certain monomial in $U$ to $0$, enough so that, for some natural number $n$, $M^n=0$. In this paper, we give a sufficient condition for a ring $R$ such that the skew monoid ring $R*M$ is quasi-Armendariz (By Hirano a ring $R$ is called...

Rosenbrock’s notion of system equivalence is general in nature; it is a kind of equivalence which in algebra is often termed as stable. We have shown recently that Fuhrmann’s notion of system equivalence can be viewed as a homotopy equivalence, and as such is also general in nature. This note deals with a generalization of the theory of system equivalences from the field case to the commutative...

In this short note we show that Stanley-Reisner rings of simplicial complexes, which have had a ‘dramatic application’ in combinatorics [2, p. 41] possess a rigidity property in the sense that they determine their underlying simplicial complexes. For the readers convenience we recall the notion of a Stanley-Reisner ring (for more information the reader is referred to [1, Ch. 5]). Let V be a fin...

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...