%0 Journal Article
%T An Application of Linear Automata to Near Rings
%A Songfa You
%A Yijun Feng
%A Ming Cao
%A Yaping Wei
%J Applied Mathematics
%P 1614-1618
%@ 2152-7393
%D 2012
%I Scientific Research Publishing
%R 10.4236/am.2012.311223
%X In this paper , we have established an intimate connection between near-nings and linear automata£¬and obtain the following results: 1) For a near-ring N there exists a linear GSA S with N ¡Õ N(S) iff (a) (N, +) is abelian, (b) N has an identity 1, (c) There is some d ¡Ê N<sub>d</sub> such that N<sub>0</sub> is generated by {1,d}; 2) Let h: S ¡ú S¡¯ be a GSA- epimorphism. Then there exists a near-ring epimorphism from N(S) to N(S¡¯) with h(qn) = h(q)h(n) for all q ¡Ê Q and n ¡Ê N(S); 3) Let A = (Q,A,B,F,G) be a GA. Then (a) A<sub>a</sub>:=(Q(N(A)) =: Q<sub>a</sub>,A,B,F/Q<sub>a</sub> ¡Á A) is accessible, (b) Q = 0N(A), (c) A/~:= (Q/~,A,B,F<sub>~</sub>), Q<sub>~</sub>) with F<sub>~</sub>([q], a):= [F(q,a)] and G<sub>~</sub>([q], a):= G(q,a) is reduced, (d) A<sub>a</sub>/~ is minimal.
%K Linear Automata
%K Accessible
%K GSA-Homomorphism
%K Near-Ring
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=24378