Biclosed relations with respect to torsion theories and almost continuous bifunctors. Issue 2 (1st February 2017)

• Record Type: Journal Article
• Authors: Fernández-Alonso, Rogelio; Cerda, Erwin
• Is Part Of: Communications in algebra. Volume 45:Issue 2(2017)
• Page Start: 889
• Page End: 909
• Publication Date: 2017-02-01
• Subjects: Adjoint functors -- biclosed relations -- bifunctors -- Galois connections -- idempotent radicals -- torsion theories; 16S90 -- 18A40 -- 06A15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1206343
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: We extend the concept of torsion theories on R -Mod, classically described using the relation ℋ defined by Ho m R ( M, N ) = 0. For each biclosed relation R with respect to ℋ, we define the conglomerate of R -torsion theories. We introduce the concepts of almost continuous (almost cocontinuous) functor, and almost continuous (AC) bifunctor, and we prove that each AC bifunctor induces a biclosed relation with respect to ℋ . We study biclosed relations induced by adjoint pairs of functors on R -Mod, which correspond to R – R -bimodules. In particular, we study biclosed relations induced by bimodules R ∕ I, and specially when R is a semisimple Artinian ring, proving that in this case the set of all biclosed relations is a Boolean lattice of 2 n 2 elements.