Goldie-like conditions on Jordan matrix rings
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- by Daniel J. Britten PDF
- Trans. Amer. Math. Soc. 190 (1974), 87-98 Request permission
Abstract:
In this paper Goldie-like conditions are put on a Jordan matrix ring $J = H({R_n},{\gamma _a})$ which are necessary and sufficient for R to be a $\ast$-prime Goldie ring or a Cayley-Dickson ring. Existing theory is then used to obtain a Jordan ring of quotients for J.References
-
D. J. Britten, On Cayley-Diekson rings, Canad. Math. Bull. Math. Notes (to appear).
—, On prime Jordan rings $H(R)$ with chain condition, J. Algebra (to appear).
- T. S. Erickson and S. Montgomery, The prime radical in special Jordan rings, Trans. Amer. Math. Soc. 156 (1971), 155–164. MR 274543, DOI 10.1090/S0002-9947-1971-0274543-4
- Nathan Jacobson, Structure of rings, Revised edition, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, Providence, R.I., 1964. MR 0222106
- 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
- Erwin Kleinfeld, Primitive alternative rings and semi-simplicity, Amer. J. Math. 77 (1955), 725–730. MR 72115, DOI 10.2307/2372593
- J. Marshall Osborn, Varieties of algebras, Advances in Math. 8 (1972), 163–369 (1972). MR 289587, DOI 10.1016/0001-8708(72)90003-5
- Chester Tsai, The prime radical in a Jordan ring, Proc. Amer. Math. Soc. 19 (1968), 1171–1175. MR 230776, DOI 10.1090/S0002-9939-1968-0230776-X
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 190 (1974), 87-98
- MSC: Primary 17A15
- DOI: https://doi.org/10.1090/S0002-9947-1974-0349772-4
- MathSciNet review: 0349772