Peirce gradings of Jordan systems
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- by José A. Anquela and Teresa Cortés
- Proc. Amer. Math. Soc. 130 (2002), 2543-2551
- DOI: https://doi.org/10.1090/S0002-9939-02-06346-3
- Published electronically: March 12, 2002
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Abstract:
In this paper we prove that the diagonal components $V_0$ and $V_2$ of a Peirce grading of a Jordan pair or triple system $V$, inherit strong primeness, primitivity and simplicity from $V$.References
- Alain D’Amour, Quadratic Jordan systems of Hermitian type, J. Algebra 149 (1992), no. 1, 197–233. MR 1165208, DOI 10.1016/0021-8693(92)90013-C
- Alain D’Amour and Kevin McCrimmon, The local algebras of Jordan systems, J. Algebra 177 (1995), no. 1, 199–239. MR 1356368, DOI 10.1006/jabr.1995.1294
- José A. Anquela and Teresa Cortés, Primitive Jordan pairs and triple systems, J. Algebra 184 (1996), no. 2, 632–678. MR 1409234, DOI 10.1006/jabr.1996.0280
- José A. Anquela and Teresa Cortés, Primitivity in Jordan systems is ubiquitous, J. Algebra 202 (1998), no. 1, 295–314. MR 1614222, DOI 10.1006/jabr.1997.7274
- J. A. Anquela, T. Cortés, “Local and Subquotient Inheritance of Simplicity in Jordan Systems". J. Algebra 240 (2001), 680–704.
- José A. Anquela, Teresa Cortés, Ottmar Loos, and Kevin McCrimmon, An elemental characterization of strong primeness in Jordan systems, J. Pure Appl. Algebra 109 (1996), no. 1, 23–36. MR 1386811, DOI 10.1016/0022-4049(95)00086-0
- Ottmar Loos, Jordan pairs, Lecture Notes in Mathematics, Vol. 460, Springer-Verlag, Berlin-New York, 1975. MR 0444721
- Ottmar Loos and Erhard Neher, Complementation of inner ideals in Jordan pairs, J. Algebra 166 (1994), no. 2, 255–295. MR 1279257, DOI 10.1006/jabr.1994.1151
- I. M. Sheffer, Some properties of polynomial sets of type zero, Duke Math. J. 5 (1939), 590–622. MR 81
- Kevin McCrimmon and Ephim Zel′manov, The structure of strongly prime quadratic Jordan algebras, Adv. in Math. 69 (1988), no. 2, 133–222. MR 946263, DOI 10.1016/0001-8708(88)90001-1
- Erhard Neher, Involutive gradings of Jordan structures, Comm. Algebra 9 (1981), no. 6, 575–599. MR 608506, DOI 10.1080/00927878108822603
Bibliographic Information
- José A. Anquela
- Affiliation: Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo s/n, 33007 Oviedo, Spain
- Email: anque@pinon.ccu.uniovi.es
- Teresa Cortés
- Affiliation: Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo s/n, 33007 Oviedo, Spain
- Email: cortes@pinon.ccu.uniovi.es
- Received by editor(s): June 16, 2000
- Received by editor(s) in revised form: April 16, 2001
- Published electronically: March 12, 2002
- Additional Notes: This work was partially supported by the DGES, PB97-1069-C02-02 and the Ministerio de Ciencia y Tecnología, BFM2001-1938-C02-02
- Communicated by: Lance W. Small
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2543-2551
- MSC (2000): Primary 17C27, 17C10, 17C20
- DOI: https://doi.org/10.1090/S0002-9939-02-06346-3
- MathSciNet review: 1900860
Dedicated: Dedicated to the memory of Eulalia García Rus