کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9493431 1334241 2005 32 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A Galois theory of commutative rings
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A Galois theory of commutative rings
چکیده انگلیسی
Galois objects-Galois groups, rings, Lie rings, and birings G-act on commutative rings A and satisfy Galois correspondence theorems which support Galois descent. This generalizes the Galois theory of fields to a Galois theory of commutative rings. In particular, the classical correspondence of Galois, the Jacobson-Bourbaki correspondence [N. Jacobson, Lectures in Algebra, vol. 3, Van Nostrand, 1964; D.J. Winter, The Jacobson descent theorem, Pacific J. Math. 104 (2) (1983) 495-496; D.J. Winter, The Structure of Fields, Springer-Verlag, 1974], the Jacobson differential correspondence [N. Jacobson, op. cit.; D.J. Winter, The Structure of Fields, op. cit.], the Galois birings correspondence of [D.J. Winter, The Structure of Fields, op. cit.], and corresponding theories of Galois descent [N. Jacobson, Forms of algebras, Yeshiva Sci. Confs. 7 (1966) 41-71; D.J. Winter, The Jacobson descent theorem, op. cit.; D.J. Winter, The Structure of Fields, op. cit.] generalize from fields to commutative rings. The Galois Lie rings correspondence Theorem 4.2 solves the simple restricted irreducible derivation rings Problem 8.4 in the finitely generated case.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 289, Issue 2, 15 July 2005, Pages 380-411
نویسندگان
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