About weakly Bézout rings
Resumo
In this paper, we examine the transfer of the proprety weakly Bézout to the trivial ring extensions. These results provide examples of weakly Bézout rings that are not Bézout rings. We show that the proprety weakly Bézout is not stable under finite direct products. Also, the class of 2- Bézout rings and class of coherent rings are not comparable with the class of weakly Bézout rings.
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Referências
D. D. Anderson, M. Winders, Idealization of a module, Rocky Mountain J. Math, 1(1), 3-56, (2009). https://doi.org/10.1216/JCA-2009-1-1-3
A. Azizi and A. Nikseresht, Simplified radical formula in modules, Houston Journal of Mathematics, 38 (2), 333-344, (2012).
C. Bakkari and K. Ouarghi, On 2-Bezout Rings, Internationnal Journal of Algebra, Vol. 4(no. 5), 241-245, (2010).
E. Bastida and R. Gilmer, Over rings and divisorial ideals of rings of the form D + M, Michigan Math. J. 20, 79-95, (1973). https://doi.org/10.1307/mmj/1029001014
D. Costa, Parameterizing families of non-Noetherian rings, Comm. Algebra 22 no. 10, 3997-4011, (1994). https://doi.org/10.1080/00927879408825061
L. Gillman and M. Henriksen, Some remarks about elementary divisor rings, Trans. Amer. Math. Soc. 82, 362-365, (1956). https://doi.org/10.1090/S0002-9947-1956-0078979-8
S. Glas, Commutative Coherent rings, Lecture Notes in Mathematics, 1371, Springer-Verlag, Berlin, (1989). https://doi.org/10.1007/BFb0084570
H. Huckaba, Commutative rings with zero divisors, Marcel Dekker, New York, (1988).
S. Kabbaj and N. Mahdou, Trivial extensions defined by coherent-like conditions, Comm. Algebra 32(10), 3937-3953, (2004). https://doi.org/10.1081/AGB-200027791
I. Kaplansky, Elementary divisors and modules, Proc. Amer. Math. Soc. 66, 464-491, (1949). https://doi.org/10.1090/S0002-9947-1949-0031470-3
M. D. Larsen, W. J. Lewis, and T. S. Shores , Elementary divisors rings and finitely presented modules, American Mathematical society, vol. 187 231 - 248, (1974). https://doi.org/10.1090/S0002-9947-1974-0335499-1
I. Palmer, J-E. Roos, Explicit formulae for the global homological dimensions of trivial extensions of rings, J. Algebra 27, 380-413, (1973). https://doi.org/10.1016/0021-8693(73)90113-0
J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, (1979).
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