210
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Factorization of elements in noncommutative rings, II

ORCID Icon & ORCID Icon
Pages 2928-2946 | Received 19 Apr 2017, Published online: 15 Dec 2017

References

  • Abrams, G., Mantese, F., Tonolo, A. Leavitt path algebras are Bézout. Preprint, arXiv:1605.08317.
  • Bessenrodt, G., Brungs, H. H., Törner, G. (1990). Right Chain Rings, Part 1. Schriftenreihe des Fachbereichs Mathematics, Vol. 181. Germany: Universität Duisburg.
  • Birkhoff, G. (1967). Lattice Theory, 3rd ed. Providence, RI: American Mathematical Society.
  • Cohn, P. M. (1963). Noncommutative unique factorization domains. Trans. Am. Math. Soc. 109:313–331.
  • Cohn, P. M. (1968). Bezout rings and their subrings. Proc. Camb. Phil. Soc. 64:251–264.
  • Cohn, P. M. (1973). Unique factorization domains. Am. Math. Monthly 801–18.
  • Cohn, P. M. (1985). Free Rings and Their Relations, 2nd ed. London Mathematical Society Monographs, Vol. 19. London, New York: Academic Press.
  • Cohn, P. M. (2006). Free Ideal Rings and Localization in General Rings. New Mathematical Monographs, Vol. 3. Cambridge: Cambridge University Press.
  • Facchini, A. (1998) Module Theory. Endomorphism Rings and Direct Sum Decompositions in Some Classes of Modules. Progress in Mathematics, Vol. 167. Basel: Birkäuser Verlag. Reprinted in Modern Birkhäuser Classics, Birkhäuser Verlag, Basel, 2010.
  • Facchini, A., Fassina, M. (2016). Factorization of elements in noncommutative rings, I. Algebra Discrete Math. 14: 209–232.
  • Goodearl, K. R. (1991). von Neumann Regular Rings, 2nd ed. Malabar, FL: Robert E. Krieger Publishing Co., Inc.
  • Grätzer, G. (1998). General Lattice Theory, 2nd ed. Basel: Birkhäuser Verlag.
  • Grätzer, G., Nation, J. B. (2011). A new look at the Jordan-Holder theorem for semimodular lattices. Algebra Universalis 64:309–311.
  • Hashimoto, J. (1948). On the product decomposition of partially ordered sets. Math. Japonicae 1:120–123.
  • Herbera, D. (2003). Bezout and hereditary power series rings. J. Algebra 270:150–168.
  • Jacobson, N. (1943). The Theory of Rings. New York: American Mathematical Society.
  • Jategaonkar, A. V. (1969). A counter-example in ring theory and homological algebra. J. Algebra 12:418–440.
  • Nakayama, T., Hashimoto, J. (1950). On a problem of G. Birkhoff. Proc. Am. Math. Soc. 1:141–142.
  • Newman, M. (1972). Integral Matrices. Pure and Applied Mathematics, Vol. 45. New York, London: Academic Press.
  • Stenström, B. (1975). Rings of Quotients. New York, Heidelberg: Springer-Verlag.
  • Tuganbaev, A. (2002). Rings Close to Regular. Mathematics and Its Applications, Vol. 545. Dordrecht: Kluwer Academic Publishers.

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:

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:

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.