Öz
In this paper, copure-injective modules is examined from an alternative perspective. For two modules A and B, A is called B-subcopure-injective if for every
copure monomorphism f : B → C and homomorphism g : B → A, there exists a
homomorphism h : C → A such that hf=g. For a module A, the
subcopure-injectivity domain of A is defined to be the collection of all
modules B such that A is B-subcopure-injective. Basic properties of the notion of subcopure-injectivity are investigated. We obtain
characterizations for various types of rings and modules, including copure-injective modules, right CDS rings and right V-rings in terms of subcopure-injectivity domains. Since
subcopure-injectivity domains clearly contains all copure-injective modules,
studying the notion of modules which are subcopure-injective only with respect
to the class of copure-injective modules is reasonable. We refer to these
modules as sc-indigent. We studied the properties of subcopure-injectivity
domains and of sc-indigent modules and investigated over some certain rings.
Anahtar Kelimeler
Copure-injective modules subcopure-injectivity domains sc-indigent modules CDS rings
Kaynakça
- Anderson, F. W., Fuller, K. R., Rings and categories of modules, Springer-Verlag, New York, 1974.
- Aydoğdu, P., López-Permouth, S. R., An alternative perspective on injectivity of modules, J. Algebra, 338 (2011) 207-219.
- Durğun, Y., An alternative perspective on flatness of modules, J. Algebra Appl., 15(8) (2016) 1650145, 18. communiserial : Fieldhouse, D. J., Pure theories, Math. Ann., 184 (1969) 1-18.
- Harmanci, A., López-Permouth, S. R., Üngör, B., On the pure-injectivity profile of a ring, Comm. Algebra , 43(11) (2015) 4984-5002.
- Hiremath, V. A., Cofinitely generated and cofinitely related modules, Acta Math. Acad. Sci. Hungar., 39 (1982), 1-9.
- Hiremath (Madurai), V. A., Copure Submodules, Acta Math. Hung., 44(1-2) (1984) 3-12.
- Hiremath (Madurai), V. A., Copure-injective modules, Indian J. Pure Appl. Math., 20(3) (1989) 250-259.
- Hiremath (Madurai), V. A., Co-absolutely co-pure modules, Proceedings of the Edinburgh Mathematical Society, 29 (1986), 289-298.
- Jans, J. P., On co-noetherian rings, J. London Math. Soc., 1 (1969), 588-590.
- López-Permouth, S. R., Mastromatteo, J., Tolooei, Y., Üngör, B., Pure-injectivity from a different perspective, Glasg. Math. J., 60(1) (2018), 135--151.
- López-Permouth, S. R., Simental-Rodriguez, J. E., Characterizing rings in terms of the extent of the injectivity and projectivity of their modules, J. Algebra, 362 (2012), 56-69.
- Mao, L., Ding, N., Notes On Cotorsion Modules, Comm. Algebra, 33 (2005), 349-360.
- Sharpe, D. W., Vamos, P., Injective Modules, (Cambridge Tracts in Mathematics and Mathematical Physics, 62), Cambridge, 1972.
- Toksoy, S. E., Modules with minimal copure-injectivity domain, J. Algebra Appl., 18(11) (2019), 195-201.
- Vamos, P., The dual of the notion of finitely generated, J. London Math. Soc., 43 (1968), 643-646.
- Vamos, P., Classical rings, J. Algebra, 34 (1975), 114-129.
Öz
Kaynakça
- Anderson, F. W., Fuller, K. R., Rings and categories of modules, Springer-Verlag, New York, 1974.
- Aydoğdu, P., López-Permouth, S. R., An alternative perspective on injectivity of modules, J. Algebra, 338 (2011) 207-219.
- Durğun, Y., An alternative perspective on flatness of modules, J. Algebra Appl., 15(8) (2016) 1650145, 18. communiserial : Fieldhouse, D. J., Pure theories, Math. Ann., 184 (1969) 1-18.
- Harmanci, A., López-Permouth, S. R., Üngör, B., On the pure-injectivity profile of a ring, Comm. Algebra , 43(11) (2015) 4984-5002.
- Hiremath, V. A., Cofinitely generated and cofinitely related modules, Acta Math. Acad. Sci. Hungar., 39 (1982), 1-9.
- Hiremath (Madurai), V. A., Copure Submodules, Acta Math. Hung., 44(1-2) (1984) 3-12.
- Hiremath (Madurai), V. A., Copure-injective modules, Indian J. Pure Appl. Math., 20(3) (1989) 250-259.
- Hiremath (Madurai), V. A., Co-absolutely co-pure modules, Proceedings of the Edinburgh Mathematical Society, 29 (1986), 289-298.
- Jans, J. P., On co-noetherian rings, J. London Math. Soc., 1 (1969), 588-590.
- López-Permouth, S. R., Mastromatteo, J., Tolooei, Y., Üngör, B., Pure-injectivity from a different perspective, Glasg. Math. J., 60(1) (2018), 135--151.
- López-Permouth, S. R., Simental-Rodriguez, J. E., Characterizing rings in terms of the extent of the injectivity and projectivity of their modules, J. Algebra, 362 (2012), 56-69.
- Mao, L., Ding, N., Notes On Cotorsion Modules, Comm. Algebra, 33 (2005), 349-360.
- Sharpe, D. W., Vamos, P., Injective Modules, (Cambridge Tracts in Mathematics and Mathematical Physics, 62), Cambridge, 1972.
- Toksoy, S. E., Modules with minimal copure-injectivity domain, J. Algebra Appl., 18(11) (2019), 195-201.
- Vamos, P., The dual of the notion of finitely generated, J. London Math. Soc., 43 (1968), 643-646.
- Vamos, P., Classical rings, J. Algebra, 34 (1975), 114-129.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Research Article |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2020 |
| Gönderilme Tarihi | 31 Ekim 2019 |
| Kabul Tarihi | 17 Nisan 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 69 Sayı: 1 |
Kaynak Göster
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
