Volume 20, Issue 2 (9-2025)
IJMSI 2025, 20(2): 155-159 |
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Danchev P, Samiei M. The Probability When a Finite Commutative Ring Is (Weakly) Nil-Neat. IJMSI 2025; 20 (2) :155-159
URL: http://ijmsi.ir/article-1-2140-en.html
URL: http://ijmsi.ir/article-1-2140-en.html
Abstract:
We study the probability of (weak) nil-neatness of a finite commutative ring, which is a natural continuation of the probabilities of (weak) nil-cleanliness that are investigated in [4, 5].
Type of Study: Research paper |
Subject:
General
References
1. M. F. Atiyah, I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, MA, 1969.
2. P. V. Danchev, W. Wm. McGovern, Commutative Weakly Nil Clean Unital Rings, J. Algebra, 425(5), (2015), 410-422. [DOI:10.1016/j.jalgebra.2014.12.003]
3. P. Danchev, M. Samiei, Commutative Weakly Nil-Neat Rings, Novi Sad J. Math., 50(2), (2020), 51-59. [DOI:10.30755/NSJOM.09638]
4. P. Danchev, M. Samiei, The Probability When a Finite Commutative Ring Is Nil-Clean, Trans. A. Razmadze Math. Inst., 176(1), (2022), 29-35. [DOI:10.1142/S1793557122501844]
5. P. Danchev, M. Samiei, The Probability When a Finite Commutative Ring Is Weakly Nil-Clean, Asian-Eur. J. Math., 15(11), (2022), 2250184(10 pages). [DOI:10.1142/S1793557122501844]
6. A. J. Diesl, Nil Clean Rings, J. Algebra, 383, (2013), 197-211. [DOI:10.1016/j.jalgebra.2013.02.020]
7. M. Samiei, Commutative Rings Whose Proper Homomorphic Images Are Nil Clean, Novi Sad J. Math., 50(1), (2020), 37-44. [DOI:10.30755/NSJOM.08071]
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