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2018 | OriginalPaper | Chapter

Coherence in Bi-amalgamated Algebras Along Ideals

Authors : Mounir El Ouarrachi, Najib Mahdou

Published in: Homological and Combinatorial Methods in Algebra

Publisher: Springer International Publishing

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Abstract

Let \(f: A\longrightarrow B\) and \(g: A\longrightarrow C\) be two ring homomorphisms and let J (resp., \(J'\)) be an ideal of B (resp., C) such that \(f^{-1}(J)=g^{-1}(J')\). In this paper, we investigate the transfer of the property of coherence in the bi-amalgamation of A with (B, C) along \((J,J')\) with respect to (f, g) (denoted by \(A\bowtie ^{f,g}(J,J'))\), introduced and studied by Kabbaj, Louartiti, and Tamekkante in 2013. We provide necessary and sufficient conditions for \(A\bowtie ^{f,g}(J,J')\) to be a coherent ring.

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previous chapter Weakly Finite Conductor Property in Amalgamated Algebra

next chapter On the Set of Intermediate Artinian Subrings

Aloui Ismaili, K., Mahdou, N.: Coherence in amalgamated algebra along an ideal. Bull Iranian Math. Soc. 41(3), 1–9 (2015)

Barucci, V., Anderson, D.F., Dobbs, D.E.: Coherent Mori domains and the principal ideal theorem. Comm. Algebra 15, 1119–1156 (1987)MathSciNetCrossRefMATH

Boisen, M.B., Sheldon, P.B.: CPI-extension: Over rings of integral domains with special prime spectrum. Canad. J. Math. 29, 722–737 (1977)MathSciNetCrossRefMATH

Brewer, W., Rutter, E.: \(D+M\) constructions with general overrings. Michigan Math. J. 23, 33–42 (1976)MathSciNetCrossRefMATH

Chhiti, M., Jarrar, M., Kabbaj, S., Mahdou, N.: Prüfer conditions in an amalgamated duplication of a ring along an ideal. Commun. Algebra 43(1), 249–261 (2015)

Costa, D.: Parameterizing families of non-Noetherian rings. Commun. Algebra 22, 3997–4011 (1994)MathSciNetCrossRefMATH

D’Anna, M.: A construction of Gorenstein rings. J. Algebra 306(2), 507–519 (2006)MathSciNetCrossRefMATH

D’Anna, M., Fontana, M.: amalgamated duplication of a ring along a multiplicative-canonical ideal. Ark. Mat. 45(2), 241–252 (2007)MathSciNetCrossRefMATH

D’Anna, M., Fontana, M.: An amalgamated duplication of a ring along an ideal: the basic properties. J. Algebra Appl. 6(3), 443–459 (2007)MathSciNetCrossRefMATH

10.

D’Anna, M., Finocchiaro, C.A., Fontana, M.: Amalgamated algebras along an ideal. In: Commutative Algebra and Applications, Proceedings of the Fifth International Fez Conference on Commutative Algebra and Applications, Fez, Morocco. W. de Gruyter Publisher, Berlin, pp. 155–172 (2009)

11.

D’Anna, M., Finocchiaro, C.A., Fontana, M.: Properties of chains of prime ideals in amalgamated algebras along an ideal. J. Pure Appl. Algebra 214, 1633–1641 (2010)MathSciNetCrossRefMATH

12.

Dobbs, D.E., Kabbaj, S., Mahdou, N., Sobrani, M.: When is \(D+M\) \(n\)-coherent and an \((n,d)\)-domain. Lecture Notes in Pure and Applications and Mathematics, Dekker, vol. 205, pp. 257–270 (1999)

13.

Dobbs, D.E., Papick, I.: When is \(D+M\) coherent. Proc. Am. Math. Soc. 56, 51–54 (1976)MathSciNetMATH

14.

Gabelli, S., Houston, E.: Coherent like conditions in pullbacks. Michigan Math. J. 44, 99–123 (1997)MathSciNetCrossRefMATH

15.

Glaz, S.: Commutative Coherent Rings. Lecture Notes in Mathematics, vol. 1371. Springer, Berlin (1989)

16.

Glaz, S.: Finite conductor rings. Proc. Am. Math. Soc. 129, 2833–2843 (2000)MathSciNetCrossRefMATH

17.

Glaz, S.: Controlling the Zero-Divisors of a Commutative Ring. Lecture Notes in Pure and Applications and Mathematics, vol. 231, pp. 191–212. Dekker (2003)

18.

Huckaba, J.A.: Commutative Rings with Zero Divisors. Marcel Dekker, New York-Basel (1988)MATH

19.

Kabbaj, S., Louartiti, K., Tamekkente, M.: Bi-amalgmeted algebras along ideals. J. Commun. Algebra 9(1), 65–87 (2017)CrossRefMATH

20.

Kabbaj, S., Mahdou, N.: Trivial extensions defined by coherent-like conditions. Commun. Algebra 32(10), 3937–3953 (2004)MathSciNetCrossRefMATH

21.

Nagata, M.: Local Rings. Interscience, New York (1962)MATH

22.

Rotman, J.J.: An Introduction to Homological Algebra. Academic Press, New York (1979)MATH

Title: Coherence in Bi-amalgamated Algebras Along Ideals
Authors: Mounir El Ouarrachi
Najib Mahdou
Publisher: Springer International Publishing
Book: Homological and Combinatorial Methods in Algebra
Print ISBN: 978-3-319-74194-9

Electronic ISBN: 978-3-319-74195-6

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-74195-6_13

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