About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Öztürk Sözen, Esra ; Eryılmaz, Figen ; Nişancı Türkmen, Burcu
On module classes of generalized semiperfect modules. (English). Mathematica Bohemica, vol. 151 (2026), issue 2, pp. 249-272
MSC: 16D10, 16D99 | DOI: 10.21136/MB.2025.0053-24
Keywords:
co-coatomic submodules; Rad-cc-supplemented modules; totally Rad-cc-supplemented modules
Summary:
We introduce Rad-cc-supplemented module which generalizes the general concept of co-coatomically-supplemented modules; a module $W$ is Rad-cc-supplemented if each co-coatomic submodule of $W$ has a Rad-supplement in $W$. In Section 2, we present various properties of these modules. In Section 3, we examine the characterization of modules over commutative domains. In Section 4, we explore the concept of $\oplus $-Rad-cc-supplemented modules, which generalizes a generalized notion of $\oplus $-co-coatomically-supplemented modules in R. Alizade, S. Güngör (2018). A module $W$ is $\oplus $-Rad-cc-supplemented if each co-coatomic $A\leq W$ is of a Rad-supplement which is a direct summand of $W$. In the concluding section of this paper, we investigate into its characteristics by introducing Rad-cc-semiperfect modules.
References:
[1] Alizade, R., Bilhan, G., Smith, P. F.: Modules whose maximal submodules have supplements. Commun. Algebra 29 (2001), 2389-2405. DOI 10.1081/AGB-100002396 | MR 1845118 | Zbl 0989.16001
[2] Alizade, R., Güngör, S.: Co-coatomically supplemented modules. Ukr. Math. J. 69 (2017), 1007-1018. DOI 10.1007/s11253-017-1411-x | MR 3689283 | Zbl 1417.16004
[3] Alizade, R., Güngör, S.: $\oplus$-co-coatomically supplemented and co-coatomically semiperfect modules. Hacet. J. Math. Stat. 47 (2018), 1417-1426. DOI 10.15672/hjms.20154413844 | MR 3974519 | Zbl 1488.16019
[4] Büyükaşik, E., Lomp, C.: On a recent generalization of semiperfect rings. Bull. Aust. Math. Soc. 78 (2008), 317-325. DOI 10.1017/S0004972708000774 | MR 2466867 | Zbl 1159.16015
[5] Büyükaşik, E., Mermut, E., Özdemir, S.: Rad-supplemented modules. Rend. Semin. Mat. Univ. Padova 124 (2010), 157-177. DOI 10.4171/RSMUP/124-10 | MR 2752682 | Zbl 1246.16007
[6] Büyükaşik, E., Tribak, R.: On $w$-local modules and Rad-supplemented modules. J. Korean Math. Soc. 51 (2014), 971-985. DOI 10.4134/JKMS.2014.51.5.971 | MR 3254569 | Zbl 1318.16008
[7] Türkmen, H. ÇalışıcıE.: Generalized $\oplus$-supplemented modules. Algebra Discrete Math. 10 (2010), 10-18. MR 2884740 | Zbl 1212.16013
[8] Clark, J., Lomp, C., Vanaja, N., Wisbauer, R.: Lifting Modules: Supplements and Projectivity in Module Theory. Frontiers in Mathematics. Birkhäuser, Boston (2006). DOI 10.1007/3-7643-7573-6 | MR 2253001 | Zbl 1102.16001
[9] Ecevit, Ş., Koşan, M. T., Tribak, R.: Rad-$\oplus$-supplemented modules and cofinitely Rad-$\oplus$-supplemented modules. Algebra Colloq. 19 (2012), 637-648. DOI 10.1142/S1005386712000508 | MR 2999271 | Zbl 1288.16006
[10] Harmanci, A., Keskin, D., Smith, P. F.: On $\oplus$-supplemented modules. Acta Math. Hung. 83 (1999), 161-169. DOI 10.1023/A:1006627906283 | MR 1682909 | Zbl 0933.16008
[11] Kasch, F.: Modules and Rings. London Mathematical Society Monographs 17. Academic Press, New York (1982). MR 0667346 | Zbl 0523.16001
[12] Keskin, D., Smith, P. F., Xue, W.: Rings whose modules are $\oplus$-supplemented. J. Algebra 218 (1999), 470-487. DOI 10.1006/jabr.1998.7830 | MR 1705802 | Zbl 0942.16004
[13] Koşan, M. T.: Generalized cofinitely semiperfect modules. Int. Electron. J. Algebra 5 (2009), 58-69. DOI 10.1080/15501320802554588 | MR 2471379 | Zbl 1193.16003
[14] Michler, G. O., Villamayor, O. E.: On rings whose simple modules are injective. J. Algebra 25 (1973), 185-201. DOI 10.1016/0021-8693(73)90088-4 | MR 0316505 | Zbl 0258.16023
[15] Mohamed, S. H., Müller, B. J.: Continuous and Discrete Modules. London Mathematical Society Lecture Note Series 147. Cambridge University Press, Cambridge (1990). DOI 10.1017/CBO9780511600692 | MR 1084376 | Zbl 0701.16001
[16] Nisanci, B., Pancar, A.: On generalization of $\oplus$-cofinitely supplemented modules. Ukr. Math. J. 62 (2010), 203-209. DOI 10.1007/s11253-010-0344-4 | MR 2888590 | Zbl 1209.16006
[17] Smith, P. F.: Finitely generated supplemented modules are amply supplemented. Arab. J. Sci. Eng., Sect. C, Theme Issues 25 (2000), 69-79. MR 1829220 | Zbl 1271.16007
[18] Türkmen, E., Pancar, A.: On cofinitely Rad-supplemented modules. Int. J. Pure Appl. Math. 53 (2009), 153-162. MR 2531535 | Zbl 1189.16003
[19] Türkmen, E., Pancar, A.: Characterizations of Rad-supplemented modules. Miskolc Math. Notes 13 (2012), 569-580. DOI 10.18514/MMN.2012.397 | MR 3002652 | Zbl 1274.13037
[20] R. B. Warfield, Jr.: Decomposability of finitely presented modules. Proc. Am. Math. Soc. 25 (1970), 167-172. DOI 10.1090/S0002-9939-1970-0254030-4 | MR 0254030 | Zbl 0204.05902
[21] Wisbauer, R.: Foundations of Module and Ring Theory: A Handbook for Study and Research. Algebra, Logic and Applications 3. Gordon and Breach Science Publishers, Philadelphia (1991). DOI 10.1201/9780203755532 | MR 1144522 | Zbl 0746.16001
[22] Xue, W.: Characterization of semiperfect and perfect rings. Publ. Mat., Barc. 40 (1996), 115-125. DOI 10.5565/PUBLMAT_40196_08 | MR 1397010 | Zbl 0863.16014
[23] Zöschinger, H.: Komplementierte Moduln über Dedekindringen. J. Algebra 29 (1974), 42-56 German. DOI 10.1016/0021-8693(74)90109-4 | MR 0340347 | Zbl 0277.13008
[24] Zöschinger, H.: Koatomare Moduln. Math. Z. 170 (1980), 221-232 German. DOI 10.1007/BF01214862 | MR 0564202 | Zbl 0411.13009
Partner of
EuDML logo