Publication Date:
1983-01-01
Description:
IfMis a centered operand over a semigroupS, the suboperands ofMcontaining zero are characterized in terms ofS-homomorphisms ofM. Some properties of centered operands over a semigroup with zero are studied.AΔ-centralizerCof a setMand the semigroupS(C,Δ)of transformations ofMoverCare introduced, whereΔis a subset ofM. WhenΔ=M,Mis a faithful and irreducible centered operand overS(C,Δ). Theorems concerning the isomorphisms of semigroups of transformations of setsMioverΔi-centralizersCi,i=1,2are obtained, and the following theorem in ring theory is deduced: LetLi,i=1,2be the rings of linear transformations of vector spaces(Mi,Di)not necessarily finite dimensional. Thenfis an isomorphism ofL1→L2if and only if there exists a1−1semilinear transformationhofM1ontoM2such thatfT=hTh−1for allT∈L1.
Print ISSN:
0161-1712
Electronic ISSN:
1687-0425
Topics:
Mathematics
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