A Bi-amalgamations of semiclean rings
Resumen
This paper establishes necessary and suficient conditions for a bi-amalgamation to inherit the semiclean (resp. UU, resp. periodic) property. Our results generalize previous studies on amalgamations and, generate examples which enrich literature with new and original families of rings satisfying the above mentioned-properties.
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C. Bakkari and M. Es-Saidi, Nil-clean property in amalgamated algebras along an ideal, Annali dell’universita di ferrara, (2018).
C. Bakkari, M. Es-Saidi, N. Mahdou et al, Extension of semiclean rings, Czech Math J 72, 461-476, (2022).
M. B. Boisen and P. B. Sheldon, CPI-extension: overrings of integral domains with special prime spectrum, Can. J. Math. 29, 722-737, (1977).
G. Calugareanu, UU rings, Carpathian J. Algebra Appl. 31, 157-163, (2015).
M. Chhiti and L. Es-Salhi, Clean-like properties in bi-amalgamation algebras, Sao Paulo Journal of Mathematical Sciences, 1-8, (2022).
M. Chhiti, M. Jarrar, S. Kabbaj and N. Mahdou, Pr¨ufer conditions in an amalgamated duplication of a ring along an ideal, Comm. Algebra 43(1), 249-261, (2015).
M. Chhiti, N. Mahdou and M. Tamekkante, Clean property in amalgamated algebras along an ideal, Hacettepe J. Math. Stat. 44(1), 41-49, (2015).
M. Chhiti and S. Moindze, Nil-clean and weakly nil-clean properties in Bi-Amalgamated algebras along ideals, Palestine Journal of Mathematics 11(2), 551-560, (2022).
P. V. Danchev and T.Y. Lam, Rings with unipotent units, Publ. Math. Debrecen 88, 449-466, (2016).
M. D’Anna, A construction of Gorenstein rings, J. Algebra 306(2), 507-519, (2006).
M. D’Anna, C. A. Finacchiaro and M. Fontana, Amalgamated algebras along an ideal, Comm Algebra and Aplications, Walter De Gruyter, 241-252, (2009).
M. D’Anna, C. A. Finacchiaro, and M. Fontana, Properties of chains of prime ideals in amalgamated algebras along an ideal, J. Pure Appl. Algebra 214, 1633-1641, (2010).
M. D’Anna and M. Fontana, An amalgamated duplication of a ring along an ideal: the basic properties, Journal of Algebra and its Applications 6(3), 443-459, (2007).
M. D’Anna and M. Fontana, The amalgamated duplication of a ring along a multiplicative-canonical ideal, Ark. Mat. 45(2), 241-252, (2007).
A. J. Diesl, Nil clean rings, J. Algebra 383, 197-211, (2013).
A. El Khalfi, H. Kim and N. Mahdou, Amalgamation extension in commutative ring theory, a survey, Moroccan Journal of Algebra and Geometry with Applications 1(1), 139-182, (2022).
C. Finocciaro and M. Fontana, Pr¨ufer-like conditions on an amalgamated algebra along an ideal, Houston J. Math. 40(1), 63-79, (2014).
S. Glaz, Commutative coherent rings, Springer-Verlag, Lecture Notes in Mathematics 1371, (1989).
J. Han and W. K. Nicholson, Extensions of clean rings, Communication in Algebra 29(6), 2589-2595, (2001).
J. A. Huckaba, Commutative rings with zero divisors, Marcel Dekker, New York-Basel, 1998.
S. Kabbaj, K. Louartiti and M. Tamekkante, Bi-amalgamated algebras along ideals, J. Commut. Algebra, 65-87, (2017).
M. Kabbour, Trivial ring extensions and amalgamations of periodic rings, J. Commut. Algebra, 65-87, (2017).
D. Khurana, Lifting potent elements modulo nil ideals, Journal of Pure and Applied Algebra 225(11), 106762, (2021).
H. Maimani and S. Yassemi, Zero-divisor graphs of amalgamated duplication of a ring along an ideal: the basic properties, J. Pure Appl. Algebra 212(1), 168-174, (2008).
W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229, 278-279, (1977).
M. Ohori, On strongly π-regular rings and periodic rings, Math. J. Okayama Univ. 27, 49-52, (1985).
J. Shapiro, On a construction of Gorenstein rings proposed by M. D’Anna, J. Algebra 323(4), 1155-1158, (2010).
Y. Ye, Semiclean rings, Comm. Alg. 31, 5609-5625, (2003).
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