Noncommutative Jordan algebras containing minimal inner ideals
Annales scientifiques de l'Université de Clermont. Mathématiques, Tome 97 (1991) no. 27, p. 153-176
@article{ASCFM_1991__97_27_153_0,
     author = {Fern\'andez L\'opez, Antonio},
     title = {Noncommutative Jordan algebras containing minimal inner ideals},
     journal = {Annales scientifiques de l'Universit\'e de Clermont. Math\'ematiques},
     publisher = {UER de Sciences exactes et naturelles de l'Universit\'e de Clermont},
     volume = {97},
     number = {27},
     year = {1991},
     pages = {153-176},
     zbl = {0851.17003},
     mrnumber = {1164719},
     language = {en},
     url = {http://www.numdam.org/item/ASCFM_1991__97_27_153_0}
}
Fernández López, Antonio. Noncommutative Jordan algebras containing minimal inner ideals. Annales scientifiques de l'Université de Clermont. Mathématiques, Tome 97 (1991) no. 27, pp. 153-176. https://www.numdam.org/item/ASCFM_1991__97_27_153_0/

1 J.C. Alexander, Compact Banach algebras. Proc. London Math. Soc. (3) 18 (1968), 1-18. | MR 229040 | Zbl 0184.16502

2 E.M. Alfen, F.W. Shultz and E. Stormer, A Gelgand Neumark theorem for Jordan algebras. Advances in Math. 28 (1978), 11-56. | MR 482210 | Zbl 0397.46065

3 W. Ambrose, Structures theorems for a special class of Banach algebra. Trans. Amer. Math. Soc. 57 (1945), 364-386. | MR 13235 | Zbl 0060.26906

4 B.A. Barnes, Modular annihilator algebras. Canad. J. Math.18 (1966), 566-578. | MR 194471 | Zbl 0156.04003

5 B.A. Barnes, On the existence of minimal ideals in Banach algebras. Trans. Amer. Math. Math. Soc. 133 (1968), 511-517. | MR 226418 | Zbl 0159.18501

6 B.A. Barnes, Examples of modular annihilator algebras. Rocky Mountain J. Math. 1 (1971), 657-665. | MR 288581 | Zbl 0233.46068

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). | Zbl 0534.46034

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. | Zbl 0692.46044

9 F.F. Bonsall and J. Duncan, Complete Normed Algebras. Springer Verlag (1973). | MR 423029 | Zbl 0271.46039

10 J.A. Cuenca Mira and A. Rodriguez Palacios, Structure theory for noncommutative Jordan H*-algebras. J. Algebra (to appear). | Zbl 0616.46047

11 J. Dieudonne, Sur le socle d'un anneau et les anneaux simples infinis. Bull. Sco. Math. de France, 71 (1943), 1-30. | JFM 68.0049.02 | Numdam | MR 46356 | Zbl 0060.07203

12 A. Fernandez Lopez, Modular annihilator Jordan algebras. Commun. in Algebra 13 (12) (1985), 2597-2613. | MR 811525 | Zbl 0613.17015

13 A. Fernandez Lopez, Ideals in nondegenerate noncommutative Jordan algebras. Commun. in Algebra, (to appear). | MR 837273 | Zbl 0591.17002

14 A. Fernandez Lopez, Noncommutative Jordan algebras coinciding with its socle. Preprint. | MR 837273

15 A. Fernandez Lopez and A. Rodriguez Palacios, On the socle of a noncommutative Jordan algebra. Submitted to Manuscripta Mathematica. | Zbl 0598.17001

16 A. Fernandez Lopez, Noncommutative Jordan Riesz algebras. Preprint. | MR 929796 | Zbl 0684.46042

17 A. Fernandez Lopez, Theoremas de Wedderburn-Zorn en algebras alterntivas normadas completas. Tesis Doctoral. Universidad de Granada. Granada 1983.

18 A. Fernandez Lopez and Rodriguez Palacios, Primitive non commutative Jordan algebras with nonzero socle. Proc. Amer. Math. Soc. 96 (2) (1986), 199-206. | MR 818443 | Zbl 0585.17001

19 A. Fernandez Lopez and Rodriguez Palacios, A Wedderbum theorem for nonassociative complete normed algebras. Proc. London Math. Soc. (to appear). | Zbl 0603.46056

20 A. Fernandez Lopez and Rodriguez Palacios, Coincidence of the socle and the maximal regular ideal in associative and Jordan Banach algebras. Preprint.

21 L. Hogben and K. Mccrimmon, Maximal modular inner ideals and the Jacobson radical of a Jordan algebra. J. Algebra 68 (1981), 155-169. | MR 604300 | Zbl 0449.17011

22 N. Jacobson, On the theory of primitive rings. Ann. of Math. 48 (1947) 8-21. | MR 19591 | Zbl 0029.10601

23 N. Jacobson, Lecture in Abstract Algebra II, Linear Algebra, New York, 1953. | Zbl 0053.21204

24 N. Jacobson, Structure of rings. Amer. Math. Sco. Colloq. Publ. 37, Providence R.I. 1964. | MR 222106 | Zbl 0073.02002

25 N. Jacobson, Structure and representations of Jordan algebras. Amer. Math. Soc. Colloq. Publ. 39, Providence R.I. 1968. | MR 251099 | Zbl 0218.17010

26 N. Jacobson and C.E. Rickart, Homomorphisms of Jordan rings of self-adjoint elements. Trans. Amer. Math. Soc. 72 (1952), 310-322. | MR 46346 | Zbl 0046.25603

27 A.M. Kaidi, Bases para una teoria de las algebras no-associativas normadas. Tesis Doctoral. Universidad de Granada. Granada 1977.

28 K. Kaplansky, Normed algebras. Duke Math. J. 16 (1949), 399-418. | MR 31193 | Zbl 0033.18701

29 E. Kleinfeld, Primitive alternative rings and semisimplicity. Amer. J. Math. 77 (4) (1955), 725-730. | MR 72115 | Zbl 0066.02302

30 K Mccrimmon, A note on quasi-associative algebras. Proc. Amer. Math. Soc. 17 (1966), 1455-1459. | MR 238910 | Zbl 0146.26002

31 K Mccrimmon, On Herstein's theorem relating Jordan and associative algebras. J. Algebra 13 (19690), 382-392. | MR 249476 | Zbl 0224.16027

32 K Mccrimmon, Noncommutative Jordan rings, Trans. Amer. Math. Soc. 158 (1971), 1-33. | MR 310024 | Zbl 0229.17002

33 K Mccrimmon, Zelmanov's prime theorem for quadratic Jordan algebras. J. Algebra 76 (1982), 297-326. | MR 661857 | Zbl 0486.17008