کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6414210 | 1630447 | 2016 | 75 صفحه PDF | دانلود رایگان |
In this paper we investigate the connection between the Mac Lane (co)homology and Wieferich primes in finite localizations of global number rings. Following the ideas of Polishchuk-Positselski [29], we define the Mac Lane (co)homology of the second kind of an associative ring with a central element. We compute these invariants for finite localizations of global number rings with an element w and obtain that the result is closely related to the Wieferich primes to the base w. In particular, for a given non-zero integer w, the infiniteness of Wieferich primes to the base w turns out to be equivalent to the following: for any positive integer n, we have HMLII,0(Z[1n!],w)â Q.As an application of our technique, we identify the ring structure on the Mac Lane cohomology of a global number ring and compute the Adams operations (introduced in this case by McCarthy [26]) on its Mac Lane homology.
Journal: Journal of Algebra - Volume 467, 1 December 2016, Pages 80-154