Figure 1. Relations between strongly quasi primary ideals and other classical ideals.
Figure 3.
Figure 2.
References
- M. Achraf, H. Ahmed, and B. Ali, 2-absorbing ideals in formal power series rings, Palestine J. Math. 6 (2017), no. 2, 502-506.
- D. D. Anderson, K. R. Knopp, and R. L. Lewin, Ideals generated by powers of elements, Bull. Australian Math. Soc. 49 (1994), no. 3, 373-376. https://doi.org/10.1017/S0004972700016488
- D. D. Anderson and M. Winders, Idealization of a module, J. Commutative Algebra 1 (2009), no. 1, 3-56. https://doi.org/10.1216/JCA-2009-1-1-3
- D. F. Anderson, R. Levy, and J. Shapiro, Zero-divisor graphs, von Neumann regular rings, and Boolean algebras, J. Pure Appl. Algebra 180 (2003), no. 3, 221-241. https://doi.org/10.1016/S0022-4049(02)00250-5
- D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), no. 2, 434-447. https://doi.org/10.1006/jabr.1998.7840
- M. Atiyah, Introduction to Commutative Algebra, CRC Press, 2018.
- A. Badawi, On divided commutative rings, Comm. Algebra 27 (1999), no. 3, 1465-1474. https://doi.org/10.1080/00927879908826507
- A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), no. 3, 417-429. https://doi.org/10.1017/S0004972700039344
- I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208-226. https://doi.org/10.1016/0021-8693(88)90202-5
- C. Beddani and W. Messirdi, 2-Prime ideals and their applications, J. Algebra and Its Applications 15 (2016), no. 3, 1650051. https://doi.org/10.1142/S0219498816500511
- N. Epstein and J. Shapiro, A Dedekind-Mertens theorem for power series rings, Proceedings of Amer. Math. Soc. 144 (2016), no. 3, 917-924. https://doi.org/10.1090/proc/12661
- L. Fuchs, On quasi-primary ideals, Acta Univ. Szeged. Sect. Sci. Math. 11 (1947), 174-183.
- R. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, Inc., New York, 1972.
- J. A. Huckaba, Commutative Rings with Zero Divisors, Monographs and Textbooks in Pure and Applied Mathematics, 117, Marcel Dekker, Inc., New York, 1988.
- C. Jayaram and U Tekir, von Neumann regular modules, Commun. Algebra 46 (2018), no. 5, 2205-2217. https://doi.org/10.1080/00927872.2017.1372460
- M. D. Larsen and P. J. McCarthy, Multiplicative Theory of Ideals, Academic Press, New York, 1971.
- M. Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers a division of John Wiley & Sons New York, 1962.
- S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra 31 (2003), no. 9, 4425-4443. https://doi.org/10.1081/AGB-120022801
- J. von Neumann, On regular rings, Proceedings of the National Academy of Sci. 22 (1936), no. 12, 707-713. https://doi.org/10.1073/pnas.22.12.707