An Application of Linear Automata to Near Rings  

作　　者：Songfa You Yijun Feng Ming Cao Yaping Wei 

机构地区：[1]School of Mathematics and Computer Science, Hubei University, Wuhan, China

出　　处：《Applied Mathematics》2012年第11期1614-1618,共5页应用数学（英文）

摘　　要：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 ≌ N(S) iff (a) (N, +) is abelian, (b) N has an identity 1, (c) There is some d ∈ Nd such that N0 is generated by {1,d};2) Let h: S → 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 ∈ Q and n ∈ N(S);3) Let A = (Q,A,B,F,G) be a GA. Then (a) Aa:=(Q(N(A)) =: Qa,A,B,F/Qa × A) is accessible, (b) Q = 0N(A), (c) A/~:= (Q/~,A,B,F~), Q~) with F^([q], a):= [F(q,a)] and G^([q], a):= G(q,a) is reduced, (d) Aa/~ is minimal.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 ≌ N(S) iff (a) (N, +) is abelian, (b) N has an identity 1, (c) There is some d ∈ Nd such that N0 is generated by {1,d};2) Let h: S → 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 ∈ Q and n ∈ N(S);3) Let A = (Q,A,B,F,G) be a GA. Then (a) Aa:=(Q(N(A)) =: Qa,A,B,F/Qa × A) is accessible, (b) Q = 0N(A), (c) A/~:= (Q/~,A,B,F~), Q~) with F^([q], a):= [F(q,a)] and G^([q], a):= G(q,a) is reduced, (d) Aa/~ is minimal.

关 键 词：LINEAR AUTOMATA Accessible GSA-Homomorphism NEAR-RING 

分 类 号：O1[理学—数学]