Cobasically discrete modules and generalizations of Bousfield’s exact sequence
الباحث الأول:
M. D. Crossley
الباحثين الآخرين:
N. T. Khafaja
المجلة:
Indian Journal of Pure and Applied Mathematics
تاريخ النشر:
23 يونيو، 2021
مختصر البحث:
Bousfield introduced an algebraic category of modules that reflects the structure detected by p-localized complex topological K-theory. He constructed, for any module M in this category, a natural 4-term exact sequence
, where U denotes the co-fre…
Bousfield introduced an algebraic category of modules that reflects the structure detected by p-localized complex topological K-theory. He constructed, for any module M in this category, a natural 4-term exact sequence
, where U denotes the co-free functor, right adjoint to the forgetful functor to
-modules. Clarke et al. identified the objects of Bousfield’s category as the ‘discrete’ modules for a certain topological ring A, obtained as a completion of the polynomial ring
, and simplified the construction of the Bousfield sequence in this context. We introduce the notion of ‘cobasically discrete’ R-modules as a clarification of the Clarke et al. modules, noting that these correspond to comodules over the coalgebra that R is dual to. We study analogues of the Bousfield sequence for other polynomial completion rings, noting a variety of behaviour in the last term of the sequence.
