Publication Date:
2015-01-01
Description:
LetNbe a near ring. An additive mappingF:N→Nis said to be a generalized semiderivation onNif there exists a semiderivationd:N→Nassociated with a functiong:N→Nsuch thatF(xy)=F(x)y+g(x)d(y)=d(x)g(y)+xF(y)andF(g(x))=g(F(x))for allx,y∈N. In this paper we prove that prime near rings satisfying identities involving semiderivations are commutative rings, thereby extending some known results on derivations, semiderivations, and generalized derivations. We also prove that there exist no nontrivial generalized semiderivations which act as a homomorphism or as an antihomomorphism on a 3-prime near ringN.
Print ISSN:
0161-1712
Electronic ISSN:
1687-0425
Topics:
Mathematics
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