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Abelian groups with the direct summand sum property

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Języki publikacji
EN
Abstrakty
EN
If R is an associative ring, with unity, the R- module (the abelian group) M is said to have the direct summand sum property (in short D.S.S.P.) if the sum (that is the submodule (the subgroup) of M generated by the union) of any two direct summands ofM is again a direct summand in M. The present work gives descriptions of some classes of abelian groups with this property.
Słowa kluczowe
Wydawca
Rocznik
Strony
477--491
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • "Babeş-Bolyai" University, Department of Mathematics, Str. M. Kogălniceanu, Nr. 1, 3400 Cluj-Napoca, Romania
Bibliografia
  • [1] U. Albrecht, J. Hausen, Modules with the quasi-summand intersection property, Bull. Austr. Math. Soc. 44 (1991), 189-201.
  • [2] U. Albrecht, J. Hausen, Mixed Abelian Groups with the Summand Intersection Property, Lecture Notes in Pure and Applied Math., 182, Dekker, New York, 1996, 123-132.
  • [3] D. M. Arnold, J. Hausen, A characterization of modules with the summand intersection property, Comm. Algebra 18(2) (1990), 519-528.
  • [4] L. Fuchs, Infinite Abelian Groups Theory, Vol. I-II, Academic Press, New York and London, Pure and Applied Mathematics, 36, (1970-1973).
  • [5] J. Hausen, Modules with the summand intersection property, Comm. Algebra 17 (1989), 135-148.
  • [6] F. F. Kamalov, Intersection of direct summands of abelian groups, (in Russian), Izv, Vyssh. Uchebn. Zaved. Mat. 5 (1977), 45-56.
  • [7] I. Kaplansky, Infinite Abelian Groups, Univ. Michigan Press, Ann Arbor, Michigan, 1954, 1969.
  • [8] A. Kuroş, The Groups Theory, (in Russian), Ed. Nauka, 1967.
  • [9] I. Purdea, Treatise of modern algebra, (in Romanian) Vol. 11, Editura Academiei R.S.R., Bucureşti, 1982.
  • [10] D. Vălcan, Abelian groups with the direct summand intersection property, (in Romanian), The Annual Conference of the Romanian Society of Mathematical Sciences, 1997, May 29-June 1, Bucharest, Romania, 111-120.
  • [11] D. Vălcan, Other characterizations of the abelian groups with the direct summand intersection property, Studia Univ. Babeş-Bolyai, Seria Mathematica, Vol. XLIII, Nr. 1, March 1998, 95-122.
  • [12] D. Vălcan, Subgroups and quotient groups of abelian groups with the direct summand intersection property, Sci. Bull. Nord Univ., Baia Mare, Seria Β, Fascicola Math.-Inf., Vol. XIII, Nr. 1-2, 17-32, 1997.
  • [13] D. Vălcan, Submodules and quotient modules of modules with the direct summand intersection property, Italian J. Pure Appi. Math. 7 (2000), 95-112.
  • [14] D. Vălcan, Injective modules with the direct summand intersection property, Sci. Bull. Moldavian Acad. Sci., Seria Math. 3(31) (1999), 39-50.
  • [15] D. Vălcan, On a problem of abelian groups theory, Proceedings of the Annual Meeting of the Romanian Society of Mathematical Sciences, Cluj-Napoca, 27-31 May 1998, 57-64.
  • [16] D. Vălcan, On some homomorphisms of direct sums of modules, Proceedings of A. Razmadze Math. Institute, vol. 124, 2000, 151-162.
  • [17] D. Vălcan, Modules with the direct summand sum property, (to appear in Czech. Math. Journal).
  • [18] D. Vălcan, Again on the direct sums of modules with the direct summand intersection property, (to appear in Sci. Bull, of Moldavian Academy of Sciences, Seria Mathematica).
  • [19] D. Vălcan, Again on problem of the direct summand intersection property, (to appear in Studia Univ. Babeş-Bolyai, Seria Mathematica).
  • [20] E. A. Walker, Cancellation in direct sums of groups, Proc. Amer. Math. Soc. 7 (1956), 898-902.
  • [21] G. V. Wilson, Modules with the summand intersection property, Comm. Algebra 14(1) (1986), 21-38.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA1-0044-0005
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