Algebraic lattices and nonassociative structures

López, Antonio; Rus, Eulalia

doi:10.1090/S0002-9939-98-04443-8

Algebraic lattices and nonassociative structures
HTML articles powered by AMS MathViewer

by Antonio Fernández López and Eulalia García Rus PDF

Proc. Amer. Math. Soc. 126 (1998), 3211-3221 Request permission

Abstract:

Uniform elements in algebraic lattices are studied and their relationship with some nonassociative extensions of Goldie’s Second Theorem is shown.

References

P. Crawley and R.P. Dilworth, Algebraic theory of lattices, Prentice-Hall, Inc., New Jersey, 1973.
Hassane Essannouni and Amin Kaidi, Semiprime alternative rings with a.c.c, Ring theory (Granada, 1986) Lecture Notes in Math., vol. 1328, Springer, Berlin, 1988, pp. 82–93. MR 959747, DOI 10.1007/BFb0100918
H. Essannouni and A. Kaidi, Goldie’s theorem for alternative rings, Proc. Amer. Math. Soc. 121 (1994), no. 1, 39–45. MR 1181162, DOI 10.1090/S0002-9939-1994-1181162-5
Antonio Fernández López, On annihilators in Jordan algebras, Publ. Mat. 36 (1992), no. 2A, 569–589 (1993). MR 1209824, DOI 10.5565/PUBLMAT_{3}62A92_{1}8
Antonio Fernández López and Eulalia García Rus, Prime Jordan algebras satisfying local Goldie conditions, J. Algebra 174 (1995), no. 3, 1024–1048. MR 1337183, DOI 10.1006/jabr.1995.1165
Antonio Fernández López and Eulalia García Rus, Nondegenerate Jordan algebras satisfying local Goldie conditions, J. Algebra 182 (1996), no. 1, 52–59. MR 1388857, DOI 10.1006/jabr.1996.0161
A. Fernández López, E. García Rus, M. Gómez Lozano and M. Siles Molina, Goldie Theorem for associative pairs (to appear).
A. Fernández López, E. García Rus and F. Montaner, Goldie Theory for Jordan algebras (to appear).
John Fountain and Victoria Gould, Orders in rings without identity, Comm. Algebra 18 (1990), no. 9, 3085–3110. MR 1063352, DOI 10.1080/00927879008824062
John Fountain and Victoria Gould, Orders in regular rings with minimal condition for principal right ideals, Comm. Algebra 19 (1991), no. 5, 1501–1527. MR 1111145, DOI 10.1080/00927879108824216
John Fountain and Victoria Gould, Orders in semiprime rings with minimal condition for principal right ideals, Proc. Roy. Soc. Edinburgh Sect. A 121 (1992), no. 3-4, 375–380. MR 1179826, DOI 10.1017/S0308210500027979
K.R. Goodearl, Ring theory: Nonsingular rings and modules Pure and Applied Mathematics, Marcel Dekker, New York, 1976.
Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099, DOI 10.1090/coll/039
Nathan Jacobson, Structure theory of Jordan algebras, University of Arkansas Lecture Notes in Mathematics, vol. 5, University of Arkansas, Fayetteville, Ark., 1981. MR 634508
O. Loos, Jordan pairs, Lecture Notes in Mathematics, vol 460, Springer-Verlag, Berlin and New York, 1975.
Kevin McCrimmon, Strong prime inheritance in Jordan systems, Algebras Groups Geom. 1 (1984), no. 2, 217–234. MR 760494
Kevin McCrimmon, The Zel′manov annihilator and nilpotence of the nil radical in quadratic Jordan algebras with chain conditions, J. Algebra 67 (1980), no. 1, 230–253. MR 595030, DOI 10.1016/0021-8693(80)90319-1
Erhard Neher, Jordan triple systems by the grid approach, Lecture Notes in Mathematics, vol. 1280, Springer-Verlag, Berlin, 1987. MR 911879, DOI 10.1007/BFb0078217
E. I. Zel′manov, Goldie theorems for Jordan algebras, Sibirsk. Mat. Zh. 28 (1987), no. 6, 44–52, 217 (Russian). MR 928338
E. I. Zel′manov, Goldie theorems for Jordan algebras. II, Sibirsk. Mat. Zh. 29 (1988), no. 4, 68–74, 223 (Russian); English transl., Siberian Math. J. 29 (1988), no. 4, 567–573 (1989). MR 969104, DOI 10.1007/BF00969864
K. A. Zhevlakov, A. M. Slin′ko, I. P. Shestakov, and A. I. Shirshov, Rings that are nearly associative, Pure and Applied Mathematics, vol. 104, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. Translated from the Russian by Harry F. Smith. MR 668355