On a class of Ikeda-Nakayama rings
DOI:
https://doi.org/10.5269/bspm.46098Abstract
In this work we introduce the notion of P-Ikeda-Nakayama rings (\P-IN-rings") which is in some way a generalization of the notion of IkedaNakayama rings (\IN-rings"). Then, we study the transfer of this property to trivial ring extension, localization, homomorphic image and to the direct product.
References
1. J. Abuihlail, M. Jarrar, and S. Kabbaj, Commutative rings in which every finitely generated ideal is quasi-projective, J. Pure Appl. Algebra 215 (2011), 2504-2511. https://doi.org/10.1016/j.jpaa.2011.02.008
2. D. D. Anderson, M. Winders, Idealization of a module, Rocky Mountain J. Math, 1(1)(2009), 3-56. https://doi.org/10.1216/JCA-2009-1-1-3
3. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
4. C. Bakkari, S. Kabbaj, and N. Mahdou, Trivial extensions defined by Prufer conditions, J. Pure Appl. Algebra 214 (2010), 53-60. https://doi.org/10.1016/j.jpaa.2009.04.011
5. G. F. Birkenmeier, M. Ghirati and A. Taherifar, When is a sum of annihilator ideals an annihilator ideal ? Comm. Algebra 43 (2015), 2690-2702. https://doi.org/10.1080/00927872.2014.882931
6. Birkenmeir, G. F, Park, J. K, Rizvi, S.T,: Extension of ring and Modules. Springer, New York (2013).
7. Camillo, V., Nicholson, W. K., Yousif, M. F. (2000). Ikeda- Nakayama rings. J. Algebra 226:1001-1010. https://doi.org/10.1006/jabr.1999.8217
8. R. Damiano and J. Shapiro, Commutative torsion stable rings, J. Pure Appl. Algebra 32 (1984), 21-32. https://doi.org/10.1016/0022-4049(84)90011-2
9. S. Glaz, Commutative coherent rings, Lect. Notes Math. 1371, SpringerVerlag, Berlin, 1989. https://doi.org/10.1007/BFb0084570
10. J.A. Huckaba, Commutative rings with zero divisors, Marcel Dekker, New York, 1988.
11. M. Nagata, Local Rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers, New York-London, 1962.
12. N. Mahdou, On weakly finite conductor rings, Comm. Algebra, 10 (2004), 4027-4036. https://doi.org/10.1081/AGB-200028231
13. I. Palmer, J. E. Roos, Explicit formulae for the global homological dimensions of trivial extensions of rings, J. Algebra 27 (1973), 380-413. https://doi.org/10.1016/0021-8693(73)90113-0
2. D. D. Anderson, M. Winders, Idealization of a module, Rocky Mountain J. Math, 1(1)(2009), 3-56. https://doi.org/10.1216/JCA-2009-1-1-3
3. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
4. C. Bakkari, S. Kabbaj, and N. Mahdou, Trivial extensions defined by Prufer conditions, J. Pure Appl. Algebra 214 (2010), 53-60. https://doi.org/10.1016/j.jpaa.2009.04.011
5. G. F. Birkenmeier, M. Ghirati and A. Taherifar, When is a sum of annihilator ideals an annihilator ideal ? Comm. Algebra 43 (2015), 2690-2702. https://doi.org/10.1080/00927872.2014.882931
6. Birkenmeir, G. F, Park, J. K, Rizvi, S.T,: Extension of ring and Modules. Springer, New York (2013).
7. Camillo, V., Nicholson, W. K., Yousif, M. F. (2000). Ikeda- Nakayama rings. J. Algebra 226:1001-1010. https://doi.org/10.1006/jabr.1999.8217
8. R. Damiano and J. Shapiro, Commutative torsion stable rings, J. Pure Appl. Algebra 32 (1984), 21-32. https://doi.org/10.1016/0022-4049(84)90011-2
9. S. Glaz, Commutative coherent rings, Lect. Notes Math. 1371, SpringerVerlag, Berlin, 1989. https://doi.org/10.1007/BFb0084570
10. J.A. Huckaba, Commutative rings with zero divisors, Marcel Dekker, New York, 1988.
11. M. Nagata, Local Rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers, New York-London, 1962.
12. N. Mahdou, On weakly finite conductor rings, Comm. Algebra, 10 (2004), 4027-4036. https://doi.org/10.1081/AGB-200028231
13. I. Palmer, J. E. Roos, Explicit formulae for the global homological dimensions of trivial extensions of rings, J. Algebra 27 (1973), 380-413. https://doi.org/10.1016/0021-8693(73)90113-0
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2022-01-31
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