Advanced search
Publication Cover
Communications in Algebra Volume 49, 2021 - Issue 9
Submit an article Journal homepage
230
Views
2
CrossRef citations to date
0
Altmetric
Articles

Virtually homo-uniserial modules and rings

M. Behboodia Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran;b School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, IranView further author information
,
A. Moradzadeh-Dehkordic Department of Sciences, Shahreza Campus, University of Isfahan, IranCorrespondence[email protected]
[email protected]
View further author information
&
M. Qourchi Nejadia Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, IranView further author information
Pages 3837-3849 | Received 23 Aug 2020, Accepted 18 Mar 2021, Published online: 28 Apr 2021

References

  • Anderson, F. W., Fuller, K. R. (1992). Rings and Categories of Modules, 2nd ed. Vol. 13. New York: Springer-Verlag.
  • Asgari, S., Behboodi, M. (2018). Commutative rings whose proper ideals are direct sums of uniform modules. Commun. Algebra 46(3):1277–1286. DOI: 10.1080/00927872.2017.1344690.
  • Behboodi, M., Daneshvar, A., Vedadi, M. R. (2018). Several generalizations of the Wedderburn-Artin theorem with applications. Algebr. Represent. Theor. 21(6):1333–1342. DOI: 10.1007/s10468-017-9748-2.
  • Behboodi, M., Ghorbani, A., Moradzadeh-Dehkordi, A., Shojaee, S. H. (2014). On left Köthe rings and a generalization of a Köthe-Cohen-Kaplansky theorem. Proc. Amer. Math. Soc. 142(8):2625–2631. DOI: 10.1090/S0002-9939-2014-11158-0.
  • Behboodi, M., Heidari, S. (2017). Commutative rings whose proper ideals are serial. Algebr. Represent. Theor. 20(6):1531–1544. DOI: 10.1007/s10468-017-9699-7.
  • Behboodi, M., Moradzadeh-Dehkordi, A., Qourchi Nejadi, M. (2020). Virtually uniserial modules and rings. J. Algebra 549:365–385. DOI: 10.1016/j.jalgebra.2019.11.038.
  • Behboodi, M., Moradzadeh-Dehkordi, A., Qourchi Nejadi, M. Direct sum decompositions of projective and injective modules into virtually uniserial modules, (Submitted).
  • Brandal, W. (1979). Commutative Rings Whose Finitely Generated Modules Decompose. Lecture Notes in Mathematics, 723. Berlin: Springer.
  • Cohn, P. M. (2006). Free Ideal Rings and Localization in General Rings. Cambridge: Cambridge University Press.
  • Eisenbud, D., Griffith, P. (1971). The structure of serial rings. Pacific J. Math. 36(1):109–121. DOI: 10.2140/pjm.1971.36.109.
  • Facchini, A. (1982). Commutative rings whose finitely embedded modules have injective dimension ⩽1. J. Algebra 77:467–483. DOI: 10.1016/0021-8693(82)90267-8.
  • Facchini, A., Nazemian, Z. (2017). Artinian dimension and isoradical of modules. J. Algebra 484:66–87. DOI: 10.1016/j.jalgebra.2017.03.039.
  • Facchini, A., Nazemian, Z. (2016). Modules with chain condittions up to isomorphisms. J. Algebra 453:578–601. DOI: 10.1016/j.jalgebra.2016.01.025.
  • McConnell, J. C., Robson, J. C. (2001). Noncommutative Noetherian Rings, with the Cooperation of L. W. Small, Revised Edition Graduate Studies in Mathematics, Vol. 30. Providence, RI: American Mathematical Society.
  • Nakayama, T. (1941). On Frobeniusean algebras. II. Ann. Math. 42(1):1–21. DOI: 10.2307/1968984.
  • Sharpe, D. W., Vamos, P. (1972). Injective Modules. Cambridge Tracts in Mathematics and Mathematical Physics, no. 62. London: Cambridge University Press.
  • Skornyakov, L. A. (1969). When are all modules serial? Mat. Zametki. 5:173–182.
  • Wang, F., Kim, H. (2016). Foundations of Commutative Rings and Their Modules. Singapore: Springer Nature Singapore Pte Ltd.
  • Warfield, R. B. Jr., (1975). Serial rings and finitely presented modules. J. Algebra 37(2):187–222. DOI: 10.1016/0021-8693(75)90074-5.
  • Wisbauer, R. (1991). Foundations of module and ring theory, Gordon and Branch Reading.
  • Zariski, O., Samuel, P. (1960). Commutative Algebra, Vol. I. Princeton, NJ: Van Nostrand.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.