REGULARITY OF CERTAIN SUBSEMIRINGS OF FULL MATRIX SEMIRINGS

  • N. Sirasuntorn
  • R. I. Sararnrakskul
Keywords: regular semiring, left regular semiring, right regular semiring

Abstract

For an additively commutative semiring with zero S, we letDVn(S) denote the set of all A ∈ Mn(S) of the form ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ x1 0 ··· 0 x1 0 x2 ··· x2 0 ··· ··· ··· ··· ··· 0 x2 ··· x2 0 x1 0 ··· 0 x1 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ where Mn(S) is the fulln×n matrix semiring over S. We show conditions for being regular semirings, left regular semirings, right regular semirings and intra-regular semirings of DVn(S).

Published
2020-02-05