SOME MATRIX GROUPS ADMITTING SKEW-SEMIFIELD STRUCTURE

Abstract

By a skew-semifield we mean an additively commutative semiring (S, +,·) with zero 0 such that (S \{0},·) is a group. A group G is said to admit a skew-semifield structure if there exists an operation + on G0 such that (G0,+,·) is a skew-semifield. In this paper, we characterize when some matrix groups admit a skew-semifield structure.