Czechoslovak Mathematical Journal, Vol. 72, No. 3, pp. 913-925, 2022
Weak $n$-injective and weak $n$-fat modules
Umamaheswaran Arunachalam, Saravanan Raja, Selvaraj Chelliah, Joseph Kennedy Annadevasahaya Mani
Received June 21, 2021. Published online May 5, 2022.
Abstract: We introduce and study the concepts of weak $n$-injective and weak $n$-flat modules in terms of super finitely presented modules whose projective dimension is at most $n$, which generalize the $n$-FP-injective and $n$-flat modules. We show that the class of all weak $n$-injective $R$-modules is injectively resolving, whereas that of weak $n$-flat right $R$-modules is projectively resolving and the class of weak $n$-injective (or weak $n$-flat) modules together with its left (or right) orthogonal class forms a hereditary (or perfect hereditary) cotorsion theory.
Affiliations: Umamaheswaran Arunachalam, National Institute of Technology (NIT), Warangal-506 004, TS, India, e-mail: ruthreswaran@gmail.com; Saravanan Raja, Sona College of Technology, Junction Main Road, Salem-636 005 Tamil Nadu, India, e-mail: saravananraja10@gmail.com; Selvaraj Chelliah (corresponding author), Periyar University, Palkalai Nagar, Salem-636 011, Tamil Nadu, India, e-mail: selvavlr@yahoo.com; Joseph Kennedy Annadevasahaya Mani, Pondicherry University, Chinna Kalapet, Kalapet, Puducherry-605 014, India, e-mail: kennedy.pondi@gmail.com
