Loewy Modules with Finite Loewy Invariants and Max Modules with Finite Radical Invariants

REFERENCES

• Anderson , D. W. , Fuller , K. R. ( 1992 ). Rings and Categories of Modules . Second Edition. GTM , Vol. 13. New York : Springer-Verlag .
   Google Scholar
• Bumby , T. T. ( 1965 ). Modules which are isomorphic to submodules of each other . Arch. Math. 16 : 184 – 185 .
   Google Scholar
• Camps , R. , Dicks , W. ( 1993 ). On semilocal rings . Israel J. Math. 81 : 203 – 211 .
   Web of Science ®Google Scholar
• Clark , J. ( 2000 ). On max modules. Proceedings of the 32nd Symposium on Ring Theory and Representation Theory. (Yamaguchi, 1999). Tokyo Univ. Agric. Technol. Tokyo, pp. 23–32 .
   Google Scholar
• Facchini , A. ( 1981 ). Loewy and artinian modules over commutative rings . Ann. Mat. Pura Appl. 128 : 359 – 374 .
   Web of Science ®Google Scholar
• Facchini , A. (1996). Krull-Schmidt fails for serial modules. Trans. Amer. Math. Soc. 348(11):4561–4575.
   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 : Birkhäuser Verlag .
   Google Scholar
• Facchini , A. , Herbera , D. ( 2006 ). Local morphisms and modules with a semilocal endomorphism ring . Algebr. Represent. Theory 9 : 403 – 422 .
   Web of Science ®Google Scholar
• Faith , C. ( 1999 ). Rings and Things and a Fine Array of Twentieth Century Associative Algebra . Mathematical Surveys and Monographs , Vol. 65. Providence, RI : American Mathematical Society .
   Google Scholar
• Faith , C. ( 1999 ). Quotient finite-dimensional modules with acc on subdirectly irreducible submodules are Noetherian . Comm. Algebra 27 ( 4 ): 1807 – 1810 .
   Web of Science ®Google Scholar
• Herbera , D. , Shamsuddin , A. ( 1995 ). Modules with semi-local endomorphism ring . Proc. Amer. Math. Soc. 123 : 3593 – 3600 .
   Web of Science ®Google Scholar
• Krull , W. ( 1928 ). Zur Theorie der allgemeinen Zahlringe . Math. Ann. 99 : 51 – 70 .
   Google Scholar
• Lam , T. Y. ( 1999 ). Lectures on Modules and Rings . Graduate Texts in Mathematics , Vol. 189. New York : Springer-Verlag .
   Google Scholar
• Menal , P. ( 1988 ). Cancellation modules over regular rings . In: Bueso , J. L. , Jara , P. , Torrecillas , B. Eds. Proc. Granada Ring Theory Conference . Lecture Notes in Math. , Vol. 1328. Berlin : Springer , pp. 187 – 208 .
   Google Scholar
• Shock , R. C. ( 1974 ). Dual generalizations of the artinian and noetherian conditions . Pacific J. Math. 54 : 227 – 235 .
   Web of Science ®Google Scholar
• Shores , T. S. ( 1974 ). Loewy series of modules . J. Reine Angew. Math. 265 : 183 – 200 .
   Web of Science ®Google Scholar
• Stenström , B. ( 1975 ). Rings of Quotients . Berlin-Heidelberg-New York : Springer-Verlag .
   Google Scholar
• Vámos , P. ( 1968 ). The dual of the notion of “finitely generated . J. London Math. Soc. 43 : 643 – 646 .
   Web of Science ®Google Scholar
• Wisbauer , R. ( 2004 ). Correct classes of modules . Algebra Discrete Math. 4 : 106 – 118 .
   Google Scholar
• Communicated by S. Bazzoni.
   Google Scholar