Noncommutative Jordan algebras containing minimal inner ideals

 Access to full text

 Full (PDF)

1. 1 J.C. Alexander, Compact Banach algebras. Proc. London Math. Soc. (3) 18 (1968), 1-18. Zbl0184.16502MR229040
2. 2 E.M. Alfen, F.W. Shultz and E. Stormer, A Gelgand Neumark theorem for Jordan algebras. Advances in Math.28 (1978), 11-56. Zbl0397.46065MR482210
3. 3 W. Ambrose, Structures theorems for a special class of Banach algebra. Trans. Amer. Math. Soc.57 (1945), 364-386. Zbl0060.26906MR13235
4. 4 B.A. Barnes, Modular annihilator algebras. Canad. J. Math.18 (1966), 566-578. Zbl0156.04003MR194471
5. 5 B.A. Barnes, On the existence of minimal ideals in Banach algebras. Trans. Amer. Math. Math. Soc.133 (1968), 511-517. Zbl0159.18501MR226418
6. 6 B.A. Barnes, Examples of modular annihilator algebras. Rocky Mountain J. Math.1 (1971), 657-665. Zbl0233.46068MR288581
7. 7 B.A. Barnes, G.J. Murphy, M.R.F. Smith and T.T. West, Riesz and Fredholm theory in Banach algebras. Research Notes in Mathematics. Pitman (1982). Zbl0534.46034
8. 8 M. Benslimane and A.M. Kaidi, Structure des algèbres de Jordan Banach non commutatives complexes regulières ou semisimples à spectre fini. Submitted to J. Algebra. Zbl0692.46044
9. 9 F.F. Bonsall and J. Duncan, Complete Normed Algebras. Springer Verlag (1973). Zbl0271.46039MR423029
10. 10 J.A. Cuenca Mira and A. Rodriguez Palacios, Structure theory for noncommutative Jordan H*-algebras. J. Algebra (to appear). Zbl0616.46047
11. 11 J. Dieudonne, Sur le socle d'un anneau et les anneaux simples infinis. Bull. Sco. Math. de France, 71 (1943), 1-30. Zbl0060.07203MR46356JFM68.0049.02
12. 12 A. Fernandez Lopez, Modular annihilator Jordan algebras. Commun. in Algebra13 (12) (1985), 2597-2613. Zbl0613.17015MR811525
13. 13 A. Fernandez Lopez, Ideals in nondegenerate noncommutative Jordan algebras. Commun. in Algebra, (to appear). Zbl0591.17002MR837273
14. 14 A. Fernandez Lopez, Noncommutative Jordan algebras coinciding with its socle. Preprint. MR837273
15. 15 A. Fernandez Lopez and A. Rodriguez Palacios, On the socle of a noncommutative Jordan algebra. Submitted to Manuscripta Mathematica. Zbl0598.17001
16. 16 A. Fernandez Lopez, Noncommutative Jordan Riesz algebras. Preprint. Zbl0684.46042MR929796
17. 17 A. Fernandez Lopez, Theoremas de Wedderburn-Zorn en algebras alterntivas normadas completas. Tesis Doctoral. Universidad de Granada. Granada1983. 
18. 18 A. Fernandez Lopez and Rodriguez Palacios, Primitive non commutative Jordan algebras with nonzero socle. Proc. Amer. Math. Soc.96 (2) (1986), 199-206. Zbl0585.17001MR818443
19. 19 A. Fernandez Lopez and Rodriguez Palacios, A Wedderbum theorem for nonassociative complete normed algebras. Proc. London Math. Soc. (to appear). Zbl0603.46056
20. 20 A. Fernandez Lopez and Rodriguez Palacios, Coincidence of the socle and the maximal regular ideal in associative and Jordan Banach algebras. Preprint. 
21. 21 L. Hogben and K. McCrimmon, Maximal modular inner ideals and the Jacobson radical of a Jordan algebra. J. Algebra68 (1981), 155-169. Zbl0449.17011MR604300
22. 22 N. Jacobson, On the theory of primitive rings. Ann. of Math.48 (1947) 8-21. Zbl0029.10601MR19591
23. 23 N. Jacobson, Lecture in Abstract Algebra II, Linear Algebra, New York, 1953. Zbl0053.21204
24. 24 N. Jacobson, Structure of rings. Amer. Math. Sco. Colloq. Publ. 37, Providence R.I.1964. Zbl0073.02002MR222106
25. 25 N. Jacobson, Structure and representations of Jordan algebras. Amer. Math. Soc. Colloq. Publ. 39, Providence R.I.1968. Zbl0218.17010MR251099
26. 26 N. Jacobson and C.E. Rickart, Homomorphisms of Jordan rings of self-adjoint elements. Trans. Amer. Math. Soc.72 (1952), 310-322. Zbl0046.25603MR46346
27. 27 A.M. Kaidi, Bases para una teoria de las algebras no-associativas normadas. Tesis Doctoral. Universidad de Granada. Granada1977. 
28. 28 K. Kaplansky, Normed algebras. Duke Math. J.16 (1949), 399-418. Zbl0033.18701MR31193
29. 29 E. Kleinfeld, Primitive alternative rings and semisimplicity. Amer. J. Math.77 (4) (1955), 725-730. Zbl0066.02302MR72115
30. 30 K McCrimmon, A note on quasi-associative algebras. Proc. Amer. Math. Soc.17 (1966), 1455-1459. Zbl0146.26002MR238910
31. 31 K McCrimmon, On Herstein's theorem relating Jordan and associative algebras. J. Algebra13 (19690), 382-392. Zbl0224.16027MR249476
32. 32 K McCrimmon, Noncommutative Jordan rings, Trans. Amer. Math. Soc.158 (1971), 1-33. Zbl0229.17002MR310024
33. 33 K McCrimmon, Zelmanov's prime theorem for quadratic Jordan algebras. J. Algebra76 (1982), 297-326. Zbl0486.17008MR661857