ON SUBFLAT DOMAINS OF RD-FLAT MODULES
Yıl: 2023 Cilt: 72 Sayı: 3 Sayfa Aralığı: 563 - 569 Metin Dili: İngilizce DOI: 10.31801/cfsuasmas.1229943 İndeks Tarihi: 06-10-2023
ON SUBFLAT DOMAINS OF RD-FLAT MODULES
Öz: The concept of subflat domain is used to measure how close (or far away) a module is to be flat. A right module is flat if its subflat domain is the entire class of left modules. In this note, we focus on of RD-flat modules that have subflat domain which is exactly the collection of all torsion-free modules, shortly tf-test modules. Properties of subflat domains and of tf-test modules are studied. New characterizations of left P-coherent rings and torsion-free rings by subflat domains of cyclically presented left $R$-modules are obtained.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Alahmadi, A. N., Alkan, M., L ́opez-Permouth, S. R., Poor modules: The opposite of injec- tivity, Glasgow Math. J., 52 (2010), 7-17. https://doi.org/10.1017/S001708951000025X
- [2] Alizade, R., Dur ̆gun, Y., Test modules for flatness,Rend. Semin. Mat. Univ. Padova, 137 (2017), 75-91. https://doi.org/10.4171/RSMUP/137-4
- [3] Auslander, M., Bridger, M., Stable Module Theory, American Mathematical Society, Provi- dence, 1969.
- [4] B ̈uy ̈uka ̧sık, E., Enochs, E., Rozas, J. R. G., Kafkas-Demirci, G., Rugged modules: The opposite of flatness, Comm. Algebra, 137 (2018), 764-779. https://doi.org/10.1080/00927872.2017.1327066
- [5] Couchot, F., RD-flatness and RD-injectivity, Comm. Algebra, 34(10) (2006), 3675–3689. https://doi.org/10.1080/00927870600860817,
- [6] Dauns, J., Fuchs, L., Torsion-freeness for rings with zero divisor, J. Algebra Appl., 3(3) (2004), 221–237. https://doi.org/10.1142/S0219498804000885
- [7] Eklof, P. C., Trlifaj, J., How to make Ext vanish, Bull. London Math. Soc., 33(1) (2001), 41-51. https://doi.org/10.1112/blms/33.1.41
- [8] Enochs, E. E., Jenda, O. M. G., Relative Homological Algebra, Walter de Gruyter & Co., Berlin, 2000.
- [9] Hattori, A., A foundation of torsion theory for modules over general rings, Nagoya Math. J., 17 (1960), 147–158. http://projecteuclid.org/euclid.nmj/1118800457
- [10] Holston, C., L ́opez-Permouth, S. R., Erta ̧s, N. O., Rings whose modules have max- imal or minimal projectivity domain, J. Pure Appl. Algebra, 216(3) (2012), 673–678. https://doi.org/10.1016/j.jpaa.2011.08.002
- [11] Holston, C., L ́opez-Permouth, S. R., Mastromatteo, J., Simental-Rodriguez, J. E., An al- ternative perspective on projectivity of modules, Glasgow Math. J., 57(1) (2015), 83–99. https://doi.org/10.1017/S0017089514000135
- [12] Lam, T. Y., Lectures on Modules and Rings, Springer-Verlag, New York, 1999.
- [13] Mao, L., Properties of RD-projective and RD-injective modules, Turkish J. Math., 35(2) (2011), 187–205. https://doi.org/10.3906/mat-0904-53
- [14] Mao, L., Ding, N., On divisible and torsionfree modules, Comm. Algebra, 36(2) (2008), 708– 731. https://doi.org/10.1080/00927870701724201
- [15] Rotman, J., An Introduction to Homological Algebra, Academic Press, New York, 1979.
- [16] Skljarenko, E. G., Relative homological algebra in the category of modules, Uspehi Mat. Nauk, 33(3) (1978), 85120.
- [17] Stenstr ̈om, B.T., Pure submodules, Arkiv f ̈ur Matematik, 7(2) (1967), 159–171. https://doi.org/10.1007/BF02591032
- [18] Trlifaj, J., Whitehead test modules, Trans. Amer. Math. Soc., 348(4) (1996) 1521–1554. https://doi.org/10.1090/S0002-9947-96-01494-8
- [19] Warfield, R. B., Purity and algebraic compactness for modules, Pacific J. Math., 28 (1969) 699–719. http://projecteuclid.org/euclid.pjm/1102983324
| APA | Bozkurt M, DURĞUN Y (2023). ON SUBFLAT DOMAINS OF RD-FLAT MODULES. , 563 - 569. 10.31801/cfsuasmas.1229943 |
| Chicago | Bozkurt Mücahit,DURĞUN YILMAZ ON SUBFLAT DOMAINS OF RD-FLAT MODULES. (2023): 563 - 569. 10.31801/cfsuasmas.1229943 |
| MLA | Bozkurt Mücahit,DURĞUN YILMAZ ON SUBFLAT DOMAINS OF RD-FLAT MODULES. , 2023, ss.563 - 569. 10.31801/cfsuasmas.1229943 |
| AMA | Bozkurt M,DURĞUN Y ON SUBFLAT DOMAINS OF RD-FLAT MODULES. . 2023; 563 - 569. 10.31801/cfsuasmas.1229943 |
| Vancouver | Bozkurt M,DURĞUN Y ON SUBFLAT DOMAINS OF RD-FLAT MODULES. . 2023; 563 - 569. 10.31801/cfsuasmas.1229943 |
| IEEE | Bozkurt M,DURĞUN Y "ON SUBFLAT DOMAINS OF RD-FLAT MODULES." , ss.563 - 569, 2023. 10.31801/cfsuasmas.1229943 |
| ISNAD | Bozkurt, Mücahit - DURĞUN, YILMAZ. "ON SUBFLAT DOMAINS OF RD-FLAT MODULES". (2023), 563-569. https://doi.org/10.31801/cfsuasmas.1229943 |
| APA | Bozkurt M, DURĞUN Y (2023). ON SUBFLAT DOMAINS OF RD-FLAT MODULES. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 72(3), 563 - 569. 10.31801/cfsuasmas.1229943 |
| Chicago | Bozkurt Mücahit,DURĞUN YILMAZ ON SUBFLAT DOMAINS OF RD-FLAT MODULES. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 72, no.3 (2023): 563 - 569. 10.31801/cfsuasmas.1229943 |
| MLA | Bozkurt Mücahit,DURĞUN YILMAZ ON SUBFLAT DOMAINS OF RD-FLAT MODULES. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.72, no.3, 2023, ss.563 - 569. 10.31801/cfsuasmas.1229943 |
| AMA | Bozkurt M,DURĞUN Y ON SUBFLAT DOMAINS OF RD-FLAT MODULES. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2023; 72(3): 563 - 569. 10.31801/cfsuasmas.1229943 |
| Vancouver | Bozkurt M,DURĞUN Y ON SUBFLAT DOMAINS OF RD-FLAT MODULES. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2023; 72(3): 563 - 569. 10.31801/cfsuasmas.1229943 |
| IEEE | Bozkurt M,DURĞUN Y "ON SUBFLAT DOMAINS OF RD-FLAT MODULES." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 72, ss.563 - 569, 2023. 10.31801/cfsuasmas.1229943 |
| ISNAD | Bozkurt, Mücahit - DURĞUN, YILMAZ. "ON SUBFLAT DOMAINS OF RD-FLAT MODULES". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 72/3 (2023), 563-569. https://doi.org/10.31801/cfsuasmas.1229943 |
