RESEARCH ARTICLE

Pure projective modules and FP-injective modules over Morita rings

  • Meiqi YAN ,
  • Hailou YAO
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  • College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, China

Received date: 04 Aug 2020

Accepted date: 02 Nov 2020

Published date: 15 Dec 2020

Copyright

2020 Higher Education Press

Abstract

Let Λ(0,0)=(AANBBNAB) be a Morita ring, where the bimodule homomorphisms ϕand ψ are zero. We study the finite presentedness, locally coherence, pure projectivity, pure injectivity, and FP-injectivity of modules over Λ(0,0). Some applications are then given.

Cite this article

Meiqi YAN , Hailou YAO . Pure projective modules and FP-injective modules over Morita rings[J]. Frontiers of Mathematics in China, 2020 , 15(6) : 1265 -1293 . DOI: 10.1007/s11464-020-0877-2

1
Bouchiba S, Khaloui M. Periodic short exact sequences and periodic pure-exact sequences. J Algebra Appl, 2010, 9(6): 859–870

DOI

2
Cheng F C, Yi Z. Homological Dimension of Rings. Guilin: Guangxi Normal Univ Press, 2000 (in Chinese)

3
Cohn P M. On the free product of associative rings. Math Z, 1959, 71: 380–398

DOI

4
Dauns J. Modules and Rings. New York: Cambridge Univ Press, 1994

DOI

5
Ding N Q, Chen J L. Coherent rings with finite self-FP-injective dimension. Comm Algebra, 1996, 24(9): 2963–2980

DOI

6
Ding N Q, Li Y L, Mao L X. J-coherent rings. J Algebra Appl, 2009, 8(2): 139–155

DOI

7
Gao N, Psaroudakis C. Gorenstein homological aspects of monomorphism categories via Morita rings. Algebr Represent Theory, 2017, 20(2): 487–529

DOI

8
Göbel R, Trlifaj J. Approximations and Endomorphism Algebras of Modules. De Gruyter Exp Math, Vol 41. Berlin: Walter de Gruyter GmbH Co KG, 2006

DOI

9
Green E L. On the representation theory of rings in matrix form. Pacific J Math, 1982, 100(1): 123–138

DOI

10
Green E L, Psaroudakis C. On Artin algebras arising from Morita contexts. Algebr Represent Theory, 2014, 17(5): 1485–1525

DOI

11
Haghany A, Mazrooei M, Vedadi M R. Pure projectivity and pure injectivity over formal triangular matrix rings. J Algebra Appl, 2012, 11(6): 1250107 (13 pp)

DOI

12
Kiełpiński R. On Γ-pure injective modules. Bull Acad Polon Sci Sér Sci Math Astronom Phys, 1967, 15: 127–131

13
Krylov P A, Tuganbaev A A. Modules over formal matrix rings. J Math Sci (N Y), 2010, 171(2): 248–295

DOI

14
Li W Q, Guan J C, Ouyang B Y. Strongly FP-injective modules. Comm Algebra, 2017, 45(9): 3816–3824

DOI

15
Mao L X, Ding N Q. Gorenstein FP-injective and Gorenstein flat modules. J Algebra Appl, 2008, 7(4): 491–506

DOI

16
Palmér I. The global homological dimension of semi-trivial extensions of rings. Math Scand, 1975, 37(2): 223–256

DOI

17
Pinzon K. Absolutely pure covers. Comm Algebra, 2008, 36(6): 2186–2194

DOI

18
Psaroudakis C. Homological theory of recollements of abelian categories. J Algebra, 2014, 398: 63–110

DOI

19
Stenström B. Coherent rings and FP-injective modules. J Lond Math Soc, 1970, 2: 323–329

DOI

20
Tang G H, Li C N, Zhou Y Q. Study of Morita contexts. Comm Algebra, 2014, 42(4): 1668–1681

DOI

21
Warfield R B. Purity and algebraic compactness for modules. Pacific J Math, 1969, 28: 699–719

DOI

22
Wisbauer R. Foundations of Module and Ring Theory. London: Gordon and Breach, 1991

23
Zhang X X, Chen J L. Free modules over rings of Morita contexts. J Southeast Univ Nat Sci, 2001, 31(5): 140–145 (in Chinese)

24
Zheng Y F, Huang Z Y. On pure derived categories. J Algebra, 2016, 454: 252–272

DOI

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