SEMILINEAR SPACES OVER SPECIAL SEMIRING

The main motive of this paper is to develop results for semimodules over special semiring identical to linear spaces over fields. This paper is divided into two parts; in first part we have given some preliminaries. Also we obtain analogue of ring and module theoretic concepts for special semiring. In second part we prove rank-nullity theorem in semilinear spaces over special semiring called strict semidomain. To give examples of special semirings, we have used Lattice theory.