کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8905063 | 1633764 | 2018 | 59 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Bokstein homomorphism as a universal object
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We give a simple construction of the correspondence between square-zero extensions Râ² of a ring R by an R-bimodule M and second MacLane cohomology classes of R with coefficients in M (the simplest non-trivial case of the construction is R=M=Z/p, Râ²=Z/p2, thus the Bokstein homomorphism of the title). Following Jibladze and Pirashvili, we treat MacLane cohomology as cohomology of non-additive endofunctors of the category of projective R-modules. We explain how to describe liftings of R-modules and complexes of R-modules to Râ² in terms of data purely over R. We show that if R is commutative, then commutative square-zero extensions Râ² correspond to multiplicative extensions of endofunctors. We then explore in detail one particular multiplicative non-additive endofunctor constructed from cyclic powers of a module V over a commutative ring R annihilated by a prime p. In this case, Râ² is the second Witt vectors ring W2(R) considered as a square-zero extension of R by the Frobenius twist R(1).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 324, 14 January 2018, Pages 267-325
Journal: Advances in Mathematics - Volume 324, 14 January 2018, Pages 267-325
نویسندگان
D. Kaledin,