#### Document Type

Article

#### Publication Date

2012

#### Publication Title

Rocky Mountain Journal of Mathematics

#### DOI

10.1216/RMJ-2012-42-6-1787

#### ISSN

0035-7596

#### Abstract

In [8] Salce introduced the notion of a co-torsion pair (A, B) in the category of abelian groups. But his deﬁnitions and basic results carry over to more general abelian categories and have proved useful in a variety of settings. In this article we will consider complete cotorsion pairs (C, D)in the category C(R-Mod) of complexes of left R-modules over some ring R.If(C, D) is such a pair, and if C is closed un-der taking suspensions, we will show when we regard K(C) and K(D) as subcategories of the homotopy category K(R-Mod), then the embedding functors K(C) → K(R-Mod) and K(D) → K(R-Mod) have left and right adjoints, respectively. In ﬁnding examples of such pairs, we will describe a procedure for using Hoveys results in [5] to ﬁnd a new model structure on C(R-Mod).

#### Recommended Citation

Bravo, Diego, Edgar E. Enochs, Alina Iacob, Overtoun M. G. Jenda, Juan Rada.
2012.
"Cotorsion Pairs in C(R-Mod)."
*Rocky Mountain Journal of Mathematics*, 42 (6): 1787-1802.
doi: 10.1216/RMJ-2012-42-6-1787

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/58

## Comments

© 2012 Rocky Mountain Mathematics Consortium. This is an open access article retrieved from the Rocky Mountain Journal of Mathematics. Articles older than 5 years are open access.