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Let R be a commutative ring. The zero-divisor graph of R is the (simple) graph Г(R) with vertices the nonzero zero-divisors of R, and two distinct vertices x and y are adjacent if and only if xy = 0. In this article, we investigate Г(R) when R does not have an identity, and we determine all such zero-divisor graphs with 14 or fewer vertices. [ABSTRACT FROM AUTHOR]

It is well-known that in general polynomials lose their CNS property by addition of small positive integers. We comment on a conjecture of S. Akiyama on addition of sufficiently large positive constants to CNS polynomials. [ABSTRACT FROM AUTHOR]

In this paper we point out the relationship between linear MRD-codes and various geometric objects as linearized polynomials, linear sets of P G ( n − 1 , q n ) , and generalized Segre varieties. We introduce and characterize a class of particular linear MRD-codes called F q n -linear codes with distance n − k + 1 proving that such codes are equivalent to ( n − k + 1 ) -embeddings of a canonical subgeometry. [ABSTRACT FROM AUTHOR]

We investigate the structure of polynomial matrices in connection with their reducibility by semiscalarequivalent transformations to simpler forms. We obtain a system of invariants for one class of matrices with respect to semiscalar equivalence. On this basis, we establish the almost canonical form of a matrix with respect to semiscalar equivalence. [ABSTRACT FROM AUTHOR]