TAILIEUCHUNG - (X ,Y)-Gorenstein projective and injective modules

This paper introduces and studies (X , Y )-Gorenstein projective and injective modules, which are a generalization of Enochs’ Gorenstein projective and injective modules, respectively. Our main aim is to investigate the relations among various (X ,Y )-Gorenstein projective modules. | Turkish Journal of Mathematics Research Article Turk J Math (2015) 39: 81 – 90 ¨ ITAK ˙ c TUB ⃝ doi: (X , Y )-Gorenstein projective and injective modules Qunxing PAN1,∗, Faqun CAI2 College of Finance, Nanjing Agricultural University, Nanjing, P. R. China 2 Department of Economic Management, Nanjing College of Chemical Technology, Nanjing, P. R. China 1 Received: • Accepted: • Published Online: • Printed: Abstract: This paper introduces and studies (X , Y )-Gorenstein projective and injective modules, which are a generalization of Enochs’ Gorenstein projective and injective modules, respectively. Our main aim is to investigate the relations among various (X , Y )-Gorenstein projective modules. Key words: 1 - (X , Y )-Gorenstein projective module, n - (X , Y )-Gorenstein projective module, (n, m) - (X , Y )-Gorenstein projective module, (X , Y )-Gorenstein projective module 1. Introduction Enochs and his coauthors introduced Gorenstein projective and injective modules and developed relative homological algebra. Later, many scholars further studied the classes and introduced some new classes of modules that are analogous to those of Gorenstein projective and injective modules. For example, Bennis and Mahdou [1] defined strongly Gorenstein projective and injective modules, and Ding et al. [3] defined strongly Gorenstein flat modules. A module M is called strongly Gorenstein flat if there is a Hom(−, F)-exact exact sequence · · · → P1 → P0 → P 0 → P 1 → · · · with every Pi , P i ∈ P such that M = ker(P0 → P 0 ), where P is the class of projective modules and F is the class of flat modules. In view of the contributions of Ding, Gillespie [5] called strongly Gorenstein flat modules Ding projective. In this paper, we introduce and study the classes of (X , Y )-Gorenstein projective and injective modules. If X = Y = P , then (X , Y) -Gorenstein projective modules

• Toán học
• Gorenstein projective module
• Enochs’ Gorenstein projective
• injective modules
• Homological algebra
• Injective R modules