Share This Article:

An Application of Linear Automata to Near Rings

Abstract Full-Text HTML XML Download Download as PDF (Size:126KB) PP. 1614-1618
DOI: 10.4236/am.2012.311223    2,538 Downloads   4,128 Views  

ABSTRACT

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

S. You, Y. Feng, M. Cao and Y. Wei, "An Application of Linear Automata to Near Rings," Applied Mathematics, Vol. 3 No. 11, 2012, pp. 1614-1618. doi: 10.4236/am.2012.311223.

References

[1] S. Eilenberg, “Automata, Language, and Machines,” Academic Press, New York, 1974.
[2] G. Pilz, “Near Rings,” North-Holland, Amsterdam, 1977.
[3] S. F. You, M. Cao and Y. J. Feng, “Semiautomata and Near Rings,” Quantitative Logic and Soft Computing, Vol. 5, 2012, pp. 428-431.
[4] S. F. You, H. Y. Zhao, Y. J. Feng and M. Cao, “An Application of Eulerian Graph to PI on Mn(C),” Applied Mathematics, Vol. 3, No. 7, 2012, pp. 809-811.
[5] S. F. You, “An Application of Eulerian Graph to Polynomial Identity,” IEEE Proceedings of the 2011 International Conference on Computational Intelligence and Software Engineering (CiSE 2011), Wuhan, 9-11 December 2011.
[6] S. F. You, et al., “Eulerian Graph and Polynomial Identities on Matrix Rings,” Advances in Mathematics, Vol. 32, No. 4, 2003, pp. 425-428.
[7] S. F. You, “The Primitivity of Extended Centroid Extension on Prime GPI-Rings,” Advances in Mathematics, Vol. 29, No. 4, 2000, pp. 331-336.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.