Maximal Left Ideals In Local Goldie (-1, 1) Rings
Abstract:
In this paper, we show how to reduce the study of nondegenerate local Goldie (-1, 1) rings to the strongly prime case, via the notions of uniform ideals and essential subdirect product. Also, we construct the maximal left quotient ring of (-1, 1) ring that is a left quotient ring of itself. We follow Utumi where a maximal left quotient ring is constructed as a direct limit of a partially defined homomorphism from the left ideal of R to R.
Author(s):
K Jayalakshmi, Department of Mathematics, JNTUA College of Engg., (Autonomous) JNTUA University, Anantapur 515002, A.P., India
DOI:
Keywords:
References:
A Anh. P. N., and Marki. L., left orders in regular rings with the minimum condition for principal One-sided ideals, Mathematical Proceedings of the Cambridge Philosophical Society, 109, 323-333 (1991). http://dx.doi.org/10.1017/S0305004100069784
A Anh. P. N., and Marki. L., A general theory of Fountain-Gould quotient rings, Mathematica Slovaca, 44(2), 225-235 (1994).
Beidar. K. L., and A.V.Mikhalov. A. V., Structure of nondegenerate alternative algebras, Journal of Soviet Mathematics, 47(3), 2525-2536 (1989). http://dx.doi.org/10.1007/BF01102996
Castellon Sersano. A., Ternandez Lopez. A., Garcia Martin. A., and Martin Gonzalez. C., Strongly prime alternative pairs with minimal inner ideals, Manuscript Mathematica, 90, 479-487 (1996).
http://dx.doi.org/10.1007/BF02568320
Essannouni. H., and Kaidi. A., Goldie’s theorem for alternative rings, Proceedings of American Mathematical Society, 1328, 39-45(1994).
http://dx.doi.org/10.1090/S0002-9939-1994-1181162-5
Fountain. J., and Gould. V., Orders in rings without identity, Communication in Algebra, 18(7), 3085-3110 (1990). http://dx.doi.org/10.1080/00927879008824062
Fernandez Lopez. A., and Garcia Rus. E., Algebraic Lattices and nonassociative structures, Proceedings of American Mathematical Society, 126(11), 3211-3221 (1998). http://dx.doi.org/10.1090/S0002-9939-98-04443-8
Fountain. J and Gould. V Straight left orders in rings, Quarterly Journal Mathematics (Oxford) 43 303-311 (1992).
http://dx.doi.org/10.1093/qmath/43.3.303
Gomez Lozano. G., and Siles Molina. M., (preprint) Left quotient rings of alternative rings.
Jayalakshmi. K., On (-1, 1) weakly Novikov rings Proceedings of International Symposium on Engineering And Natural Sciences (Macau) Vol. 1, Aug. (2013).
Jayalakshmi. K., A note on (-1, 1) ring satisfying a.c.c, International Journal of Algebra and Statistics Vol.3 (2), 34-41 (2014).
Zhevlokov. K. A, Slinko. A. M, Shestakov. I. P., and Shirshov. A. I. (1982). Rings that are nearly associative, Academic Press, New York.
