Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
See all formats and pricing
More options …
Ahead of print

Issues

On adjoint resolutions and dimensions of modules

Lixin Mao
  • Corresponding author
  • Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, P. R. China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-03-11 | DOI: https://doi.org/10.1515/gmj-2018-0015

Abstract

We introduce and investigate the adjoint resolutions and adjoint dimensions of modules. As a consequence, we give some new characterizations of weak global dimensions of coherent rings in terms of adjoint resolutions and adjoint dimensions of modules.

Keywords: Adjoint precover; adjoint preenvelope; adjoint resolution; adjoint dimension; weak global dimension

MSC 2010: 16D40; 16D50; 16E05; 16E10

References

  • [1]

    J. Asensio Mayor and J. Martinez Hernández, On flat and projective envelopes, J. Algebra 160 (1993), no. 2, 434–440. CrossrefGoogle Scholar

  • [2]

    M. Auslander and S. O. Smalø, Preprojective modules over Artin algebras, J. Algebra 66 (1980), no. 1, 61–122. CrossrefGoogle Scholar

  • [3]

    T. J. Cheatham and D. R. Stone, Flat and projective character modules, Proc. Amer. Math. Soc. 81 (1981), no. 2, 175–177. CrossrefGoogle Scholar

  • [4]

    J. L. Chen, P-projective modules, Comm. Algebra 24 (1996), no. 3, 821–831. CrossrefGoogle Scholar

  • [5]

    R. R. Colby, Rings which have flat injective modules, J. Algebra 35 (1975), 239–252. CrossrefGoogle Scholar

  • [6]

    N. Q. Ding, On envelopes with the unique mapping property, Comm. Algebra 24 (1996), no. 4, 1459–1470. CrossrefGoogle Scholar

  • [7]

    N. Q. Ding and J. L. Chen, Relative coherence and preenvelopes, Manuscripta Math. 81 (1993), no. 3–4, 243–262. CrossrefGoogle Scholar

  • [8]

    N. Q. Ding and J. L. Chen, On copure flat modules and flat resolvents, Comm. Algebra 24 (1996), no. 3, 1071–1081. CrossrefGoogle Scholar

  • [9]

    E. E. Enochs, Injective and flat covers, envelopes and resolvents, Israel J. Math. 39 (1981), no. 3, 189–209. CrossrefGoogle Scholar

  • [10]

    E. E. Enochs and O. M. G. Jenda, Copure injective resolutions, flat resolvents and dimensions, Comment. Math. Univ. Carolin. 34 (1993), no. 2, 203–211. Google Scholar

  • [11]

    E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, De Gruyter Exp. Math. 30, Walter de Gruyter, Berlin, 2000. Google Scholar

  • [12]

    D. J. Fieldhouse, Character modules, dimension and purity, Glasg. Math. J. 13 (1972), no. 2, 144–146. CrossrefGoogle Scholar

  • [13]

    R. Göbel and J. Trlifaj, Approximations and Endomorphism Algebras of Modules, De Gruyter Exp. Math. 41, Walter de Gruyter, Berlin, 2006. Google Scholar

  • [14]

    T. Y. Lam, Lectures on Modules and Rings, Grad. Texts in Math. 189, Springer, New York, 1999. Google Scholar

  • [15]

    J. Lambek, Lectures on Rings and Modules, Blaisdell Publishing, Waltham, 1966. Google Scholar

  • [16]

    L. X. Mao, Adjoint preenvelopes and precovers of modules, Publ. Math. Debrecen 88 (2016), no. 1–2, 139–161. CrossrefWeb of ScienceGoogle Scholar

  • [17]

    L. X. Mao and N. Q. Ding, Relative copure injective and copure flat modules, J. Pure Appl. Algebra 208 (2007), no. 2, 635–646. Web of ScienceCrossrefGoogle Scholar

  • [18]

    C. Megibben, Absolutely pure modules, Proc. Amer. Math. Soc. 26 (1970), no. 4, 561–566. Web of ScienceCrossrefGoogle Scholar

  • [19]

    J. J. Rotman, An Introduction to Homological Algebra, Pure Appl. Math. 85, Academic Press, New York, 1979. Google Scholar

  • [20]

    B. Stenström, Coherent rings and FP-injective modules, J. Lond. Math. Soc. 2 (1970), no. 2, 323–329. Google Scholar

  • [21]

    R. Wisbauer, Foundations of Module and Ring Theory. A Handbook for Study and Research, Algebra Logic Appl. 3, Gordon and Breach Science Publishers, Philadelphia, 1991. Google Scholar

  • [22]

    J. Xu, Flat Covers of Modules, Lecture Notes in Math. 1634, Springer, Berlin, 1996. Google Scholar

About the article

Received: 2016-04-23

Revised: 2016-11-21

Accepted: 2016-12-16

Published Online: 2018-03-11


Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11771202

Funding Source: Natural Science Foundation of Jiangsu Province

Award identifier / Grant number: BK20160771

Funding Source: Nanjing Institute of Technology

Award identifier / Grant number: CKJA201707

This research was supported by NSFC (No. 11771202), NSF of Jiangsu Province of China (No. BK20160771) and Nanjing Institute of Technology of China (No. CKJA201707).


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0015.

Export Citation

© 2018 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in