Research Article
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On subflat domains of RD-flat modules

Year 2023, , 563 - 569, 30.09.2023
https://doi.org/10.31801/cfsuasmas.1229943

Abstract

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.

Supporting Institution

The Scientific and Technological Research Council of Turkey (TUBITAK)

Project Number

119F176

Thanks

We thank the Scientific and Technological Council of Turkey for supporting our study with project number 119F176.

References

  • Alahmadi, A. N., Alkan, M., L´opez-Permouth, S. R., Poor modules: The opposite of injectivity, Glasgow Math. J., 52 (2010), 7-17. https://doi.org/10.1017/S001708951000025X
  • Alizade, R., Durğun, Y., Test modules for flatness, Rend. Semin. Mat. Univ. Padova, 137 (2017), 75-91. https://doi.org/10.4171/RSMUP/137-4
  • Auslander, M., Bridger, M., Stable Module Theory, American Mathematical Society, Providence, 1969.
  • Büyükaşık, 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
  • Couchot, F., RD-flatness and RD-injectivity, Comm. Algebra, 34(10) (2006), 3675–3689. https://doi.org/10.1080/00927870600860817
  • 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
  • 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
  • Enochs, E. E., Jenda, O. M. G., Relative Homological Algebra, Walter de Gruyter & Co., Berlin, 2000.
  • 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
  • Holston, C., Lopez-Permouth, S. R., Erta¸s, N. O., Rings whose modules have maximal or minimal projectivity domain, J. Pure Appl. Algebra, 216(3) (2012), 673–678. https://doi.org/10.1016/j.jpaa.2011.08.002
  • Holston, C., Lopez-Permouth, S. R., Mastromatteo, J., Simental-Rodriguez, J. E., An alternative perspective on projectivity of modules, Glasgow Math. J., 57(1) (2015), 83–99. https://doi.org/10.1017/S0017089514000135
  • Lam, T. Y., Lectures on Modules and Rings, Springer-Verlag, New York, 1999.
  • 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
  • Mao, L., Ding, N., On divisible and torsionfree modules, Comm. Algebra, 36(2) (2008), 708–731. https://doi.org/10.1080/00927870701724201
  • Rotman, J., An Introduction to Homological Algebra, Academic Press, New York, 1979.
  • Skljarenko, E. G., Relative homological algebra in the category of modules, Uspehi Mat. Nauk, 33(3) (1978), 85120.
  • Stenström, B.T., Pure submodules, Arkiv für Matematik, 7(2) (1967), 159–171. https://doi.org/10.1007/BF02591032
  • Trlifaj, J., Whitehead test modules, Trans. Amer. Math. Soc., 348(4) (1996) 1521–1554. https://doi.org/10.1090/S0002-9947-96-01494-8
  • Warfield, R. B., Purity and algebraic compactness for modules, Pacific J. Math., 28 (1969) 699–719. http://projecteuclid.org/euclid.pjm/1102983324
Year 2023, , 563 - 569, 30.09.2023
https://doi.org/10.31801/cfsuasmas.1229943

Abstract

Project Number

119F176

References

  • Alahmadi, A. N., Alkan, M., L´opez-Permouth, S. R., Poor modules: The opposite of injectivity, Glasgow Math. J., 52 (2010), 7-17. https://doi.org/10.1017/S001708951000025X
  • Alizade, R., Durğun, Y., Test modules for flatness, Rend. Semin. Mat. Univ. Padova, 137 (2017), 75-91. https://doi.org/10.4171/RSMUP/137-4
  • Auslander, M., Bridger, M., Stable Module Theory, American Mathematical Society, Providence, 1969.
  • Büyükaşık, 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
  • Couchot, F., RD-flatness and RD-injectivity, Comm. Algebra, 34(10) (2006), 3675–3689. https://doi.org/10.1080/00927870600860817
  • 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
  • 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
  • Enochs, E. E., Jenda, O. M. G., Relative Homological Algebra, Walter de Gruyter & Co., Berlin, 2000.
  • 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
  • Holston, C., Lopez-Permouth, S. R., Erta¸s, N. O., Rings whose modules have maximal or minimal projectivity domain, J. Pure Appl. Algebra, 216(3) (2012), 673–678. https://doi.org/10.1016/j.jpaa.2011.08.002
  • Holston, C., Lopez-Permouth, S. R., Mastromatteo, J., Simental-Rodriguez, J. E., An alternative perspective on projectivity of modules, Glasgow Math. J., 57(1) (2015), 83–99. https://doi.org/10.1017/S0017089514000135
  • Lam, T. Y., Lectures on Modules and Rings, Springer-Verlag, New York, 1999.
  • 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
  • Mao, L., Ding, N., On divisible and torsionfree modules, Comm. Algebra, 36(2) (2008), 708–731. https://doi.org/10.1080/00927870701724201
  • Rotman, J., An Introduction to Homological Algebra, Academic Press, New York, 1979.
  • Skljarenko, E. G., Relative homological algebra in the category of modules, Uspehi Mat. Nauk, 33(3) (1978), 85120.
  • Stenström, B.T., Pure submodules, Arkiv für Matematik, 7(2) (1967), 159–171. https://doi.org/10.1007/BF02591032
  • Trlifaj, J., Whitehead test modules, Trans. Amer. Math. Soc., 348(4) (1996) 1521–1554. https://doi.org/10.1090/S0002-9947-96-01494-8
  • Warfield, R. B., Purity and algebraic compactness for modules, Pacific J. Math., 28 (1969) 699–719. http://projecteuclid.org/euclid.pjm/1102983324
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Mücahit Bozkurt 0000-0003-3265-1994

Yilmaz Durğun 0000-0002-1230-8964

Project Number 119F176
Publication Date September 30, 2023
Submission Date January 10, 2023
Acceptance Date February 28, 2023
Published in Issue Year 2023

Cite

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. https://doi.org/10.31801/cfsuasmas.1229943
AMA Bozkurt M, Durğun Y. On subflat domains of RD-flat modules. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. September 2023;72(3):563-569. doi:10.31801/cfsuasmas.1229943
Chicago Bozkurt, Mücahit, and Yilmaz Durğun. “On Subflat Domains of RD-Flat Modules”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 3 (September 2023): 563-69. https://doi.org/10.31801/cfsuasmas.1229943.
EndNote Bozkurt M, Durğun Y (September 1, 2023) On subflat domains of RD-flat modules. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 3 563–569.
IEEE M. Bozkurt and Y. Durğun, “On subflat domains of RD-flat modules”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 3, pp. 563–569, 2023, doi: 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 (September 2023), 563-569. https://doi.org/10.31801/cfsuasmas.1229943.
JAMA Bozkurt M, Durğun Y. On subflat domains of RD-flat modules. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:563–569.
MLA Bozkurt, Mücahit and Yilmaz Durğun. “On Subflat Domains of RD-Flat Modules”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 3, 2023, pp. 563-9, doi:10.31801/cfsuasmas.1229943.
Vancouver Bozkurt M, Durğun Y. On subflat domains of RD-flat modules. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(3):563-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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