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modules; direct summands; sum property; Artinian rings
The present work gives some characterizations of $R$-modules with the direct summand sum property (in short DSSP), that is of those $R$-modules for which the sum of any two direct summands, so the submodule generated by their union, is a direct summand, too. General results and results concerning certain classes of $R$-modules (injective or projective) with this property, over several rings, are presented.
[1] F. W. Anderson and K. R.  Fuller: Rings and Categories of Modules. Springer-Verlag, Berlin-Heidelberg-New York, 1974. MR 0417223
[2] D. M. Arnold and J. Hausen: A characterization of modules with the summand intersection property. Comm. Algebra 18 (1990), 519–528. DOI 10.1080/00927879008823929 | MR 1047325
[3] C. Faith: Lectures on Injective Modules and Quotient Rings. Lecture Notes in Math. 49. Springer-Verlag, Berlin-Heidelberg-New York, 1967. MR 0227206
[4] L.  Fuchs: Infinite Abelian Groups, vol. I–II. Pure Appl. Math. 36. Academic Press, 1970–1973. MR 0255673
[5] J. Hausen: Modules with the summand intersection property. Comm. Algebra 17 (1989), 135–148. DOI 10.1080/00927878908823718 | MR 0970868 | Zbl 0667.16020
[6] I.  Kaplansky: Infinite Abelian Groups. Univ. of Michigan Press, Ann Arbor, Michigan, 1954, 1969. MR 0233887
[7] I. Purdea and G. Pic: Treatise of Modern Algebra, vol. I. Editura Academiei R.S.R., Bucureşti, 1977. (Romanian) MR 0490621
[8] I.  Purdea: Treatise of Modern Algebra, vol. II. Editura Academiei R.S.R., Bucureşti, 1982. (Romanian) MR 0682923
[9] J. J. Rotman: Notes on Homological Algebra. Van Nostrand Reinhold Company, New York, Cincinnati, Toronto, London, 1970. MR 0409590
[10] D. W. Sharpe and P.  Vámos: Injective Modules. Cambridge University Press, 1972. MR 0360706
[11] D.  Vălcan: Injective modules with the direct summand intersection property. Sci. Bull. of Moldavian Academy of Sciences, Seria Mathematica 31 (1999), 39–50. MR 1792906
[12] G. V.  Wilson: Modules with the summand intersection property. Comm. Algebra 14 (1986), 21–38. DOI 10.1080/00927878608823297 | MR 0814137 | Zbl 0592.13008
[13] X. H. Zheng: Characterizations of Noetherian and hereditary rings. Proc. Amer. Math. Soc. 93 (1985), 414–416. DOI 10.1090/S0002-9939-1985-0773992-0 | MR 0773992 | Zbl 0571.16010
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