ON $(m,n)$-CLOSED IDEALS IN AMALGAMATED ALGEBRA

Let [Formula: see text] and [Formula: see text] be two commutative rings with unity, let [Formula: see text] be an ideal of [Formula: see text] and [Formula: see text] be a ring homomorphism. In this paper, we give a characterization for the amalgamated algebra [Formula: see text] to be a Nagata ring, a strong S-domain, and a catenarian. Also, we investigate the conditions that the ring of Hurwitz series over [Formula: see text] has a complete comaximal factorization.

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Valuation , Weak Global Dimension and Semihereditary in Amalgamated Algebra Along an Ideal

International Journal of Open Problems in Computer Science and Mathematics ◽

10.12816/0006191 ◽

2014 ◽

Vol 7 (1) ◽

pp. 1-12

Author(s):

Moutu Abdou Salam Moutui

Keyword(s):

Global Dimension ◽

Amalgamated Algebra

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Power Serieswise Armendariz Property in Amalgamated Algebra

Bulletin of the Iranian Mathematical Society ◽

10.1007/s41980-018-0117-7 ◽

2018 ◽

Vol 45 (1) ◽

pp. 23-33

Author(s):

Mounir El Ouarrachi ◽

Najib Mahdou

Keyword(s):

Amalgamated Algebra

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The zero-divisor graph of an amalgamated algebra

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/s12215-020-00554-x ◽

2020 ◽

Author(s):

Y. Azimi ◽

M. R. Doustimehr

Keyword(s):

Zero Divisor ◽

Zero Divisor Graph ◽

Amalgamated Algebra

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Artinian ring and amalgamated algebra along an ideal

Ricerche di Matematica ◽

10.1007/s11587-019-00458-8 ◽

2019 ◽

Vol 69 (1) ◽

pp. 207-213

Author(s):

Ali Molkhasi

Keyword(s):

Artinian Ring ◽

Amalgamated Algebra

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Weakly Finite Conductor Property in Amalgamated Algebra

Homological and Combinatorial Methods in Algebra - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-3-319-74195-6_12 ◽

2018 ◽

pp. 117-126

Author(s):

Haitham El Alaoui

Keyword(s):

Amalgamated Algebra ◽

Finite Conductor

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The diameter of the zero-divisor graph of an amalgamated algebra

Collectanea mathematica ◽

10.1007/s13348-018-0236-8 ◽

2018 ◽

Vol 70 (3) ◽

pp. 399-405

Author(s):

Y. Azimi

Keyword(s):

Zero Divisor ◽

Zero Divisor Graph ◽

Amalgamated Algebra

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New Algebraic Properties of an Amalgamated Algebra Along an Ideal

Communications in Algebra ◽

10.1080/00927872.2015.1033628 ◽

2016 ◽

Vol 44 (5) ◽

pp. 1836-1851 ◽

Cited By ~ 22

Author(s):

Marco D'Anna ◽

Carmelo A. Finocchiaro ◽

Marco Fontana

Keyword(s):

Algebraic Properties ◽

Amalgamated Algebra

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WEAKLY PRIME IDEALS ISSUED FROM AMALGAMATED ALGEBRA

Hacettepe Journal of Mathematics and Statistics ◽

10.15672/hujms.557437 ◽

2019 ◽

pp. 1-9

Author(s):

Moutu Abdou Salam Moutui

Keyword(s):

Prime Ideals ◽

Amalgamated Algebra ◽

Weakly Prime Ideals

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On (n,d)-property in amalgamated algebra

Asian-European Journal of Mathematics ◽

10.1142/s1793557116500145 ◽

2016 ◽

Vol 09 (01) ◽

pp. 1650014 ◽

Cited By ~ 1

Author(s):

Karima Alaoui Ismaili ◽

Najib Mahdou

Keyword(s):

Ring Homomorphism ◽

Amalgamated Algebra

Let [Formula: see text] be a ring homomorphism and let [Formula: see text] be an ideal of [Formula: see text]. In this paper, we investigate the transfer of the [Formula: see text]-property from a ring [Formula: see text] to his amalgamated algebra [Formula: see text]. Our aim is to give new and original families of [Formula: see text]-rings which are neither [Formula: see text]-rings ([Formula: see text]) nor [Formula: see text]-rings ([Formula: see text]), and examples of [Formula: see text]-rings which are neither [Formula: see text]-rings ([Formula: see text]) nor [Formula: see text]-rings ([Formula: see text]).

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