Biring Theory and Its Galois Theory of Rings

REFERENCES

• Brzezinski , T. , Militaru , G. ( 2002 ). Bialgebroids, × A -bialgebras and duality . J. Algebra 251 ( 1 ): 279 – 294 .
   Web of Science ®Google Scholar
• Kadison , L. (2006). The endomorphism ring theorem for Galois and depth two extensions. J. Algebra 305:163–184.
   Web of Science ®Google Scholar
• Kadison , L. ( 2008 ). Finite depth and Jacobson–Bourbaki correspondence . Journal of Pure and Applied Algebra 212 ( 7 ): 1822 – 1839 .
   Web of Science ®Google Scholar
• Kennedy , C. , Winter , D. J. ( 2009 ). Depth generated simple Lie algebras . Algebras and Representation Theory 12 ( 1 ): 53 – 61 .
   Web of Science ®Google Scholar
• Lam , T. Y. ( 1999 ). Lectures on Modules and Rings . Vol. 189 . Grad. Texts in Math. , Berlin : Springer-Verlag, p. 557 .
   Google Scholar
• Lu , J. J. ( 1996 ). Hopf algebroids and quantum groupoids . Int. J. Math. 7 ( 1 ): 47 – 70 .
   Web of Science ®Google Scholar
• Szlachanyi , K. ( 2002 ). Galois actions by finite quantum groupoids. In: Leonid Vainerman, ed. Locally Compact Quantum Groups and Groupoids. Berlin: de Gruyter. Proceedings of the Meeting of Theoretical Physicists and Mathematicians, Strasbourg, February 2002 .
   Google Scholar
• Takeuchi , M. ( 1977 ). Groups of algebras over . J. Math. Soc. Japan 29 : 459 – 492 .
   Web of Science ®Google Scholar
• Winter , D. J. ( 1974 ). The Structure of Fields . Vol. 16 . Grad. Texts in Math. , Berlin : Springer-Verlag, p. 205 .
   Google Scholar
• Winter , D. J. ( 2005a ). Lie algops and simple Lie algebras . Communications in Algebra 33 ( 9 ): 3157 – 3178 .
   Web of Science ®Google Scholar
• Winter , D. J. ( 2005b ). A Galois theory of commutative rings . Journal of Algebra 289 ( 2 ): 380 – 411 .
   Web of Science ®Google Scholar
• Winter , D. J. ( 2007 ). Simple nil Lie algops . Communications in Algebra 35 ( 4 ): 1093 – 1126 .
   Web of Science ®Google Scholar
• Winter , D. J. ( 2009 ). Central simple nonassociative algebras with operators . Communications in Algebra 37 ( 11 ): 4153 – 4169 .
   Web of Science ®Google Scholar
• Winter , D. J. ( 2012 ). Primordials and primordial Lie algebras . Manuscripta Mathematica 138 : 35 – 58 .
   Web of Science ®Google Scholar
• Xu , P. ( 2001 ). Quantum groupoids . Comm. Math Phys. 216 : 539 – 581 .
   Web of Science ®Google Scholar
• Communicated by L. Small.
   Google Scholar