Rings whose modules satisfy chain conditions on essential endosubmodules

References

• Albu, T., Nastasescu, C. (1984). Relative Finiteness in Module Theory. New York - Basel: Marcel Dekker.
   Google Scholar
• Anderson, F. W., Fuller, K. R. (1992). Rings and Categories of Modules. New York: Springer-Verlag.
   Google Scholar
• Angeleri Hügel, L., Saorín, M. (2006). Modules with perfect decompositions. Math. Scand. 98:19–43.
   Web of Science ®Google Scholar
• Armendariz, E. (1980). Rings with dcc on essential left ideals. Commun. Algebra 8:299–308.
   Web of Science ®Google Scholar
• Auslander, M. (1974). Representation theory of artin algebras II. Commun. Algebra 1:269–310.
   Google Scholar
• Cozzens, J. H. (1970). Homological properties of the ring of differential polynomials. Bull. Amer. Math. Soc. 76:75–79.
   Web of Science ®Google Scholar
• Crawley-Boevey, W. W. (1991). Tame algebras and generic modules. Proc. London Math. Soc. 63:241–265.
   Web of Science ®Google Scholar
• Crawley-Boevey, W. W. (1992). Modules of finite length over their endomorphism rings. In: Brenner, S., Tachikawa, H., eds. Representations of Algebras and Related Topics, London Mathematical Society Lecture Note Series, Vol. 168. Cambridge: Cambridge University Press, pp. 127–184.
   Google Scholar
• Dung, N. V. (1999). Preinjective modules and finite representation type of artinian rings. Commun. Algebra 27:3921–3947.
   Web of Science ®Google Scholar
• Dung, N. V. (2001). Strong preinjective partitions and almost split morphisms. J. Pure Appl. Algebra 158:131–150.
   Web of Science ®Google Scholar
• Dung, N. V., García, J. L. (2001). Additive categories of locally finite representation type. J. Algebra 238:200–238.
   Web of Science ®Google Scholar
• Dung, N. V., García, J. L. (2004). Copure semisimple categories and almost split maps. J. Pure Appl. Algebra 188:73–94.
   Web of Science ®Google Scholar
• Dung, N. V., García, J. L. (2005). Endofinite modules and pure semisimple rings. J. Algebra 289:574–593.
   Web of Science ®Google Scholar
• Dung, N. V., García, J. L. (2007). Endoproperties of modules and local duality. J. Algebra 316:368–391.
   Web of Science ®Google Scholar
• Dung, N. V., García, J. L. (2012). Indecomposable modules over pure semisimple hereditary rings. J. Algebra 371:577–595.
   Web of Science ®Google Scholar
• Dung, N. V., Huynh, D. V., Smith, P. F., Wisbauer, R. (1994). Extending Modules. Pitman Research Notes in Mathematics, Vol. 313. Harlow: Longman.
   Google Scholar
• Dung, N. V., Huynh, D. V., Wisbauer, R. (1989). Quasi-injective modules with acc or dcc on essential submodules. Arch. Math. 53:252–255.
   Web of Science ®Google Scholar
• Facchini, A. (1998). Module Theory. Endomorphism Rings and Direct Sum Decompositions in Some Classes of Modules. Progress in Mathematics, Vol. 167. Basel: Springer, Birkhäuser Verlag.
   Google Scholar
• Faith, C. (1982). Injective Modules and Injective Quotient Rings. New York - Basel: Marcel Dekker.
   Google Scholar
• Fuller, K. R. (1976). On rings whose left modules are direct sums of finitely generated modules, Proc. Amer. Math. Soc. 54:39–44.
   Web of Science ®Google Scholar
• Fuller, K. R., Reiten, I. (1975). Note on rings of finite representation type and decompositions of modules. Proc. Amer. Math. Soc. 50:92–94.
   Web of Science ®Google Scholar
• Herzog, I. (1994). A test for finite representation type. J. Pure Appl. Algebra 95:151–182.
   Web of Science ®Google Scholar
• Huisgen-Zimmermann, B. (1990). Strong preinjective partitions and representation type of artinian rings. Proc. Amer. Math. Soc. 109:309–322.
   Web of Science ®Google Scholar
• Huisgen-Zimmermann, B. (2000). Purity, algebraic compactness, direct sum decompositions, and representation type. In: Infinite Length Modules (Bielefeld, 1998). Trends in Mathematics. Basel: Birkhäuser, pp. 331–367.
   Google Scholar
• Huisgen-Zimmermann, B., Zimmermann, W. (1990). On the sparsity of representations of rings of pure global dimension zero, Trans. Amer. Math. Soc. 320:695–711.
   Web of Science ®Google Scholar
• Huisgen-Zimmermann, B., Saorín, M. (2002). Direct sums of representations as modules over their endomorphism rings. J. Algebra 250:67–89.
   Web of Science ®Google Scholar
• Mohamed, S. H., Müller, B. J. (1990). Continuous and Discrete Modules. London Mathematical Society Lecture Note Series, Vol. 147. Cambridge: Cambridge University Press.
   Google Scholar
• Osofsky, B. L. (1992). Chain conditions on essential submodules. Proc. Amer. Math. Soc. 114:11–19.
   Web of Science ®Google Scholar
• Prest, M. Y. (1988). Model Theory of Modules. Cambridge: Cambridge University Press.
   Google Scholar
• Ringel, C. M., Tachikawa, H. (1975). QF-3 rings. J. Reine Angew. Math. 272:49–72.
   Web of Science ®Google Scholar
• Rowen, L. H. (1986). Finitely presented modules over semiperfect rings. Proc. Amer. Math. Soc. 97:1–7.
   Web of Science ®Google Scholar
• Simson, D. (1997). A class of potential counter-examples to the pure semisimplicity conjecture. In: Droste, M., Göbel, R., eds. Advances in Algebra and Model Theory. Algebra, Logic and Applications. Amsterdam: Gordon and Breach, pp. 345–373.
   Google Scholar
• Stenström, B. (1975). Rings of Quotients. Heidelberg - New York: Springer-Verlag.
   Google Scholar
• Teply, M. L., Miller, R. W. (1979). The descending chain condition relative to a torsion theory. Pac. J. Math. 83:207–219.
   Web of Science ®Google Scholar
• Wisbauer, R. (1991). Foundations of Module and Ring Theory. Algebra, Logic and Applications, Vol. 3. Reading: Gordon and Breach.
   Google Scholar