Signed Singular Mappings Transformation Semigroup (Published)
The semigroup of all singular self mappings of denoted by was studied by Howie (1966). Also Howie and Schein (1973) investigated the elements of . In like manner, the singular mappings in signed transformation, to be defined on the set where and In this paper the order, idempotent, nilpotent and chain decomposition of signed singular mapping were investigate.
Keywords: Chain Decomposition, Idempotent, Nilpotent, semigroup, signed full transformation., singular mapping
On Some Signed Semigroups of Order – Preserving Transformation (Published)
Let 3, .., n} and be a transformation from whereThe semigroup of (the full transformation semigroup), (the partial transformation semigroup) and (the partial one – one transformation semigroup) serve the bedrock for these transformation semigroups, Let denotes the sets of signed full order – preserving, signed partial order – preserving and signed partial one – one order – preserving transformation semigroup respectively. The paper aims at investigate the sets of these subsemigroups.
Keywords: Chain Decomposition, Idempotent, Nilpotent, Order Preserving, Self-Inverse, Transformation Semigroup