Small supplements weak supplements and proper classes
| dc.contributor.author | Engin BÜYÜKAŞIK | |
| dc.contributor.author | Rafail ALİZADE | |
| dc.contributor.author | Yılmaz DUR?GUN | |
| dc.contributor.author | Buyukasik, Engin | |
| dc.contributor.author | Durgun, Yilmaz | |
| dc.contributor.author | Alizade, Rafail | |
| dc.contributor.author | Dur?gun, Yılmaz | |
| dc.date.accessioned | 2025-10-22T16:06:18Z | |
| dc.date.issued | 2016 | |
| dc.description.abstract | Let SS denote the class of short exact sequences E :0 ->, A->, B ->,C ->, 0 of R-modules and R-module homomorphisms such that f (A)has a small supplement in B i.e. there exists a submodule K of M suchthat f (A) + K = B and f (A) ? K is a small module. It is shown that SS is a proper class over left hereditary rings. Moreover in this case the proper classSS coincides with the smallest proper class containing the class of short exact sequences determined by weak supplementsubmodules. The homological objects such as SS-projective and SScoinjective modules are investigated. In order to describe the classSS we investigate small supplemented modules i.e. the modules each ofwhose submodule has a small supplement. Besides proving some closure properties of small supplemented modules we also give a completecharacterization of these modules over Dedekind domains | |
| dc.identifier.citation | Alizade R. and Bilhan G. and Smith P. F. Modules whose maximal submodules have supplements Comm. Algebra 29 (6) 2389-2405 2001.Alizade R. and Büyükaşik E. Extensions of weakly supplemented modules Math. Scand. (2) 161-168 2008.Alizade R. and Demirci Y. and Durgun Y. and Pusat D. The Proper Class Generated by Weak Supplements Comm. Algebra 42 56-72 2014.Buchsbaum D. A. A note on homology in categories Ann. of Math. 69 66-74 1959.Büyükaşik E. and Lomp C. Rings whose modules are weakly supplemented are perfect. Applications to certain ring extensions Math. Scand. 105 (1) 25-30 2009.Clark J. and Tütüncü D. K. and Tribak R. Almost injective modules Comm. Algebra 4390-4402 2011.Clark J. and Lomp C. and Vanaja N. and Wisbauer R.Lifting modules Frontiers in Mathematics Basel 2006.Lam T. Y. Lectures on Modules and Rings New York: Springer-Verlag 1998.Leonard W. W. Small modules Proc. Amer. Math. Soc. 17 527-531 1966.Lomp C. On semilocal modules and rings Comm. Algebra 27 (4) 1921-1935 1999.Mac Lane S. Homology Academic Press Inc. New York 1963.McConnell J. C. and Robson J. C. Noncommutative Noetherian rings John Wiley & Sons Ltd. New York 1987.Mishina A. P. and Skornyakov L. A. Abelian groups and modules American Mathematical Society 1976. Nunke R. J.Purity and subfunctors of the identity Topics in Abelian Groups (Proc. Sympos. New Mexico State Univ. Scott Foresman and Co. Chicago Ill. 121-171 1963.Pancar A. Generation of proper classes of short exact sequences Internat. J. Math. Math. Sci. 20 (3) 465-473 1997. Renault G.Étude de certains anneaux A liés aux sous-modules compléments d'un A- module C. R. Acad. Sci. Paris 259 4203-4205 1964.Rotman J. J. An introduction to homological algebra Springer New York 2009.Sharpe D. W. and Vámos P.Injective modules Cambridge University Press London Skljarenko E. G. Relative homological algebra in the category of modules Uspehi Mat. Nauk 33 (3) 85-120 1978.Smith P. F. Injective modules and prime ideals Comm. Algebra 9 (3) 989-999 1981. Zöschinger H.Komplementierte Moduln über Dedekindringen J. Algebra 42-56 Zöschinger H. Koatomare Moduln Math. Z. 170 (3) 221-232 1980.Zöschinger H. Schwach-injektive Moduln Period. Math. Hungar. 52 (2) 105-128 2006. | |
| dc.identifier.doi | 10.15672/HJMS.20164512507 | |
| dc.identifier.issn | 1303-5010 | |
| dc.identifier.issn | 2651-477X | |
| dc.identifier.scopus | 2-s2.0-84978698431 | |
| dc.identifier.uri | https://gcris.yasar.edu.tr/handle/123456789/11067 | |
| dc.identifier.uri | https://search.trdizin.gov.tr/en/yayin/detay/209056 | |
| dc.identifier.uri | https://doi.org/10.15672/HJMS.20164512507 | |
| dc.language.iso | İngilizce | |
| dc.publisher | Hacettepe Univ, FAC Sci | |
| dc.relation.ispartof | Hacettepe Journal of Mathematics and Statistics | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.source | Hacettepe Journal of Mathematics and Statistics | |
| dc.subject | Matematik | |
| dc.subject | Proper Class of Short Exact Sequences | |
| dc.subject | Weak Supplement Submodule | |
| dc.subject | Small Module | |
| dc.subject | Small Supplement Submodule | |
| dc.title | Small supplements weak supplements and proper classes | |
| dc.type | Article | |
| dc.type | Article | |
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| gdc.author.id | DURĞUN, YILMAZ/0000-0002-1230-8964 | |
| gdc.author.id | Alizade, Refail/0000-0003-4444-9136 | |
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| gdc.author.wosid | DURĞUN, YILMAZ/C-3131-2018 | |
| gdc.author.wosid | Alizade, Refail/AAW-1211-2020 | |
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| gdc.description.departmenttemp | [Alizade, Rafail] Yasar Univ, Dept Math, Univ Cad 35-37, TR-35100 Izmir, Turkey; [Buyukasik, Engin] Izmir Inst Technol, Dept Math, TR-35430 Izmir, Turkey; [Durgun, Yilmaz] Bitlis Eren Univ, Dept Math, TR-13000 Bitlis, Turkey | |
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| gdc.oaire.keywords | Small module | |
| gdc.oaire.keywords | Proper class of short exact sequences;weak supplement submodule;small module;small supplement submodule | |
| gdc.oaire.keywords | Commutative rings | |
| gdc.oaire.keywords | weak supplement submodule | |
| gdc.oaire.keywords | General module theory | |
| gdc.oaire.keywords | proper class of short exact sequences | |
| gdc.oaire.keywords | small module | |
| gdc.oaire.keywords | small supplement submodule | |
| gdc.oaire.keywords | Proper class of short exact sequences | |
| gdc.oaire.keywords | Mathematical Sciences | |
| gdc.oaire.keywords | Relative homological algebra, projective classes (category-theoretic aspects) | |
| gdc.oaire.keywords | Homological functors on modules (Tor, Ext, etc.) in associative algebras | |
| gdc.oaire.keywords | General module theory in associative algebras | |
| gdc.oaire.keywords | Homological functors on modules | |
| gdc.oaire.keywords | Dedekind, Prüfer, Krull and Mori rings and their generalizations | |
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