Outer Inheritance of Simplicity in Jordan Systems

References

• D'Amour , A. 1992 . Quadratic Jordan systems of hermitian type . J. Algebra , 149 : 197 – 233 .
   Google Scholar
• D'Amour , A. and McCrimmon , K. 1995 . The local algebras of Jordan systems . J. Algebra , 177 : 199 – 239 . [CROSSREF]
   Google Scholar
• D'Amour , A. and McCrimmon , K. 2000 . The structure of quadratic Jordan systems of Clifford type . J. Algebra , 234 : 31 – 89 . [CROSSREF]
   Google Scholar
• Anquela , J. A. and Cortés , T. 1996 . Primitive Jordan pairs and triple systems . J. Algebra , 184 : 632 – 678 . [CROSSREF]
   Google Scholar
• Anquela , J. A. and Cortés , T. 2000 . Outer inheritance in Jordan systems . Comm. Algebra , 28 ( 9 ) : 4165 – 4178 .
   Google Scholar
• Anquela , J. A. and Cortés , T. 2001 . Local and subquotient inheritance of simplicity in Jordan systems . J. Algebra , 240 : 680 – 704 . [CROSSREF]
   Google Scholar
• Anquela , J. A. , Cortés , T. and García , E. 2001 . Herstein's theorems and simplicity of hermitian Jordan systems . J. Algebra , 246 : 193 – 214 . [CROSSREF]
   Google Scholar
• Anquela , J. A. , Cortés , T. and García , E. 2002 . Simplicity of the heart of a nondegenerate Jordan system . J. Pure Appl. Algebra , 172 : 119 – 137 . [CROSSREF]
   Google Scholar
• Anquela , J. A. , Cortés , T. , Loos , O. and McCrimmon , K. 1996 . An elemental characterization of strong primeness in Jordan systems . J. Pure Appl. Algebra , 109 : 23 – 36 . [CROSSREF]
   Google Scholar
• Anquela , J. A. , Cortés , T. and Montaner , F. 1995 . The structure of primitive quadratic Jordan algebras . J. Algebra , 172 : 530 – 553 .
   Google Scholar
• Fernández-López , A. , García Rus , E. , Gómez-Lozano , M. and Siles-Molina , M. 1998 . Goldie theorems for associative pairs . Comm. Algebra , 26 ( 9 ) : 2987 – 3020 .
   Google Scholar
• García , E. and Neher , E. to appear . Semiprime, prime and simple Jordan superpairs covered by grids J. Algebra
   Google Scholar
• Jacobson , N. 1956 . Structure of Rings Vol. 37 , Providence , Rhode Island : Amer. Math. Soc. Colloquium Publications .
   Google Scholar
• Jacobson , N. 1975 . PI-Algebras , Lecture Notes in Mathematics Vol. 441 , New York : Springer-Verlag .
   Google Scholar
• Lewand , R. and McCrimmon , K. 1970 . Macdonald's theorem for quadratic Jordan algebras . Pacific J. Math. , 35 : 681 – 707 .
   Google Scholar
• Loos , O. 1975 . Jordan Pairs , Lecture Notes in Mathematics Vol. 460 , New York : Springer-Verlag .
   Google Scholar
• Loos , O. 1989 . On the socle of a Jordan pair . Collect. Math. , 40 : 109 – 125 .
   Google Scholar
• McCrimmon , K. 1969 . On Herstein's theorems relating Jordan and associative algebras . J. Algebra , 13 : 382 – 392 . [CROSSREF]
   Google Scholar
• McCrimmon , K. 1970 . The Freudenthal-Springer-Tits construction revisited . Trans. Amer. Math. Soc. , 148 : 293 – 314 .
   Google Scholar
• McCrimmon , K. 1999a . Jordan centroids . Comm. Algebra , 27 ( 2 ) : 933 – 954 .
   Google Scholar
• McCrimmon , K. 1999b . Outer inheritance in Jordan algebras . Comm. Algebra , 27 ( 12 ) : 6127 – 6145 .
   Google Scholar
• McCrimmon , K. and Zelmanov , E. 1988 . The structure of strongly prime quadratic Jordan algebras . Adv. Math. , 69 ( 2 ) : 133 – 222 .
   Google Scholar
• Meyberg , K. 1972 . Lectures on Algebras and Triple Systems , Lecture Notes Charlottesville , Virginia : University of Virginia .
   Google Scholar
• Montaner , F. 1999 . Local PI theory of Jordan systems . J. Algebra , 216 : 302 – 327 . [CROSSREF]
   Google Scholar
• Neher , E. 1987 . Jordan Triple Systems by the Grid Approach , Lecture Notes in Mathematics Vol. 1280 , Berlin : Springer-Verlag .
   Google Scholar
• Rowen , L. 1988 . Ring Theory Vol. I , New York : Academic Press .
   Google Scholar
• Zelmanov , E. I. 1983 . Prime Jordan triple systems . Siberian Math. J. , 24 : 23 – 67 .
   Google Scholar
• #Communicated by B. Allison.
   Google Scholar