When is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>X</mml:mi><mml:mi>B</mml:mi><mml:mo stretchy="false">[</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">]</mml:mo><mml:mo stretchy="false">]</mml:mo></mml:math> Noetherian?

Hizem, Sana; Benhissi, Ali

doi:10.1016/j.crma.2004.11.017

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Pullback Constructions1

Noetherian Rings and Related Rings1

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2009

2023

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Cited by 11 publications

(2 citation statements)

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“…Note that S. Hizem and A. Benhissi [12] have already given a characterization of the Noetherianity of the power series rings of the form A C XBOEOEX . We preserve the notation of As a consequence of the previous proposition, we can characterize when rings of the form A C XBOEX and A C XBOEOEX are Noetherian.…”

Section: Pullback Constructionsmentioning

confidence: 99%

Amalgamated algebras along an ideal

D'Anna¹,

Finocchiaro²,

Fontana³

2009

Commutative Algebra and Its Applications

104

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Let f W A ! B be a ring homomorphism and J an ideal of B. In this paper, we initiate a systematic study of a new ring construction called the "amalgamation of A with B along J with respect to f ". This construction finds its roots in a paper by J. L. Dorroh appeared in 1932 and provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced and studied by D'Anna and Fontana in 2007, and other classical constructions such as the A C XBOEX and A C XBOEOEX constructions, the CPI-extensions of Boisen and Sheldon, the D C M constructions and the Nagata's idealization.

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Section: Pullback Constructionsmentioning

confidence: 99%

Amalgamated algebras along an ideal

D'Anna¹,

Finocchiaro²,

Fontana³

2009

Commutative Algebra and Its Applications

104

View full text Add to dashboard Cite

show abstract

“…In [10,[12][13][14], the authors characterized when composite rings R C XDOEOEX and R C XDOEX are Noetherian rings, S-Noetherian rings, or satisfy the ascending chain condition on principal ideals. It was shown that RCXDOEOEX (resp., R C XDOEX ) is a Noetherian ring if and only if R is a Noetherian ring and D is a finitely generated R-module …”

Section: Noetherian Rings and Related Ringsmentioning

confidence: 99%