Direct Product Decomposition of Alternative Rings

Alternative Loop Rings

DRAFT Abstract The right alternative law implies the left alternative law in loop rings of characteristic other than 2. We also exhibit a loop which fails to be a right Bol loop, even though its characteristic 2 loop rings are right alternative.

Schur rings over a product of Galois rings

The recently developed theory of Schur rings over a finite cyclic group is generalized to Schur rings over a ring R being a product of Galois rings of coprime characteristics. It is proved that if the characteristic of R is odd, then as in the cyclic group case any pure Schur ring over R is the tensor product of a pure cyclotomic ring and Schur rings of rank 2 over non-fields. Moreover, it is s...

The Diameter of a Zero-divisor Graph for Finite Direct Product of Commutative Rings

This paper establishes a set of theorems that describe the diameter of a zero-divisor graph for a finite direct product R1 × R2 × · · · × Rn with respect to the diameters of the zero-divisor graphs of R1, R2, · · · , Rn−1 and Rn(n > 2).

Some Questions concerning Alternative Rings

A Note on Direct Product of Fuzzy Modules over Fuzzy Rings

In this paper, a new kind of direct product of fuzzy modules over fuzzy rings is studied by using the definition of new type of fuzzy modules over fuzzy rings which is introduced in [3]. Some properties of this new structure is investigated analogues to ordinary module theory. Mathematics Subject Classification: 03E72; 08A72, 20N25