On NN-torsion-free and NN-injective modules

References

• Ahmad, Y. D., Mahdi, R. (2016). On ϕ-Schreier ring. J. Korean Math. Soc. 53(5):1057–1075.
   Web of Science ®Google Scholar
• Anderson, D. F., Badawi, A. (2004). On ϕ-Prüfer rings and ϕ-Bezout rings. Houston J. Math. 30(2):331–343.
   Web of Science ®Google Scholar
• Anderson, D. F., Badawi, A. (2005). on ϕ-Dedekind rings and ϕ-Krull rings. Houston J. Math. 31(4):1007–1022.
   Web of Science ®Google Scholar
• Bacem, K., Benhissi, A. (2016). Nonnil-coherent rings. Beitr. Algebra Geom. 57(2):297–305. DOI: 10.1007/s13366-015-0260-8.
   Google Scholar
• Badawi, A. (1999). On ϕ-pseudo-valuation rings. In: Lecture Notes in Pure and Applied Mathematics, Vol. 205. New York, Basel: Marcel Dekker, pp. 101–110.
   Google Scholar
• Badawi, A. (2000). On ϕ-pseudo-valuation rings II. Houston J. Math. 26(3):473–480.
   Web of Science ®Google Scholar
• Badawi, A. (2001). On ϕ-chained rings and ϕ-pseudo-valuation rings. Houston J. Math. 27(4):725–736.
   Web of Science ®Google Scholar
• Badawi, A. (2002). On divided rings and ϕ-pseudo-valuation rings. In: Commutative Rings. Hauppauge, NY: Nova Science Publishers, pp. 5–14.
   Google Scholar
• Badawi, A. (2003). On nonnil-Noetherian rings. Commun. Algebra 31(4):1669–1677. DOI: 10.1081/AGB-120018502.
   Web of Science ®Google Scholar
• Badawi, A. (2009). On rings with divided nil ideal. In: Commutative Algebra and its Applications. Berlin: Walter De Gruyter, pp. 21–40.
   Google Scholar
• Badawi, A., Dobbs, D. E. (2006). Strong ring extensions and ϕ-pseudo-valuation rings. Houston J. Math. 32(2):379–398.
   Web of Science ®Google Scholar
• Badawi, A., Jaballah, A. (2008). Some finiteness conditions on the set of overrings of a ϕ-ring. Houston J. Math. 34(2):397–407.
   Web of Science ®Google Scholar
• Badawi, A., Lucas, T. (2005). Rings with prime nilradical. In: Arithmetical Properties of Commutative Rings and Monoids. Boca Raton, FL: Chapman Hall/CRC, pp. 198–212.
   Google Scholar
• Badawi, A., Lucas, T. (2006). on ϕ-Mori rings. Houston J. Math. 32(1):1–31.
   Web of Science ®Google Scholar
• Benhissi, A. (2020). Nonnil-Noetherian rings and formal power series. Algebra Colloq. 27(3):361–368. DOI: 10.1142/S1005386720000292.
   Web of Science ®Google Scholar
• Gaur, A., Kumar, R. (2022). Maximal non-Prüfer and Maximal non-ϕ-Prüfer rings. Commun. Algebra 50(4):1613–1631. DOI: 10.1080/00927872.2021.1986517.
   Web of Science ®Google Scholar
• Hizem, S., Benhissi, A. (2011). On nonnil-Noetherian rings and the SFT property. Rocky Mountain J. Math. 41(5):1483–1500. DOI: 10.1216/RMJ-2011-41-5-1483.
   Web of Science ®Google Scholar
• Khalfaoui, R. E., Mahdou, N. (2020). The ϕ-Krull dimension of some commutative extensions. Commun. Algebra 48(9):3800–3810. DOI: 10.1080/00927872.2020.1747479.
   Web of Science ®Google Scholar
• Khalfia, A. E., Kim H., Mahdou N. (2021). On ϕ-piecewise Noetherian rings. Commun. Algebra 49(3):1324–1337. DOI: 10.1080/00927872.2020.1834571.
   Web of Science ®Google Scholar
• Kim, H., Wang, F. G. (2012). On ϕ-strong Mori rings. Houston J. Math. 38(2):359–371.
   Web of Science ®Google Scholar
• Lomp, C., Sant’ana, A. (2009). Comparability, distributivity and non-commutative ϕ-rings. Repositrio Aberto U. Porto 205–214.
   Google Scholar
• Rotman, J. J. (2009). An Introduction to Homological Algebra, 2nd ed. New York: Academic Press.
   Google Scholar
• Wang, F. G., Kim, H. (2016). Foundations of Commutative Rings and their modules. Springer Nature Singapore Pte Ltd.
   Google Scholar
• Yang, X. Y., Liu, Z. K. (2009). On nonnil-Noetherian rings. Southeast Asian Bull. Math. 33(6):1215–1223.
   Google Scholar
• Zhang, X. L., Zhao, W., Wang F. G. (2021). On ϕ-flat cotorsion theory. J. Guangxi Normal Univ. 39(2):119–124.
   Google Scholar
• Zhao, W. (2015). A few kinds of commutative rings with the nilradical as prime ideal. J. Neijiang Normal Univ. 30(6):11–14.
   Google Scholar
• Zhao, W. (2018). On ϕ-flat modules and ϕ-Prüfer rings. J. Korean Math. Soc. 55(5):1221–1233.
   Web of Science ®Google Scholar
• Zhao, W. (2021). On ϕ-exact sequences and ϕ-projective modules. J. Korean Math. Soc. 58(6):1513–1528.
   Web of Science ®Google Scholar
• Zhao, W., Wang, M. Q., Pu, Y. Y. (2022). On nonnil-commutative diagrams and nonnil-projective modules. Commun. Algebra 50(7):2854–2867. DOI: 10.1080/00927872.2021.2021223.
   Web of Science ®Google Scholar
• Zhao, W., Wang, F. G., Tang, G. H. (2013). On ϕ-von Neumann regular rings. J. Korean Math. Soc. 50(1):219–229. DOI: 10.4134/JKMS.2013.50.1.219.
   Web of Science ®Google Scholar
• Zhao, W., Wang, F. G., Zhang, X. L. (2020). On ϕ-projective modules and ϕ-Prüfer rings. Commun. Algebra 48(7):3079–3090. DOI: 10.1080/00927872.2020.1729362.
   Web of Science ®Google Scholar
• Zhao, W., Zhang, X. L. (2019). On nonnil-injective modules. J. Sichuan Normal Univ. 42(6):808–815.
   Google Scholar