Amalgamated duplication of some special rings along an ideal

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TAVASOLI E.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2018 | Volume:4 | Issue:15 Page(s): 31-38

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Information Journal Paper

Title

Amalgamated duplication of some special rings along an ideal

Author(s)

TAVASOLI E. | Issue Writer Certificate

Keywords

Extension of ring along an idealQ1

Generically GorensteinQ1

Generically Cohen-MacaulayQ1

Approximately GorensteinQ1

Approximately Cohen-MacaulayQ1

Abstract

Let be a commutative Noetherian ring and let I be a proper ideal of. D’ Anna and Fontana in [6] introduced a new construction of ring, named amalgamated duplication of along I. In this paper by considering the ring homomorphism, it is shown that if, then, also it is proved that if, then there exists such that. Using this result it is shown that if is Generically Cohen-Macaulay (resp. Generically Gorenstein) and is generically maximal Cohen-Macaulay (resp. a generically canonical module), then is Generically Cohen-Macaulay (resp. Generically Gorenstein). We also defined the notion of generically quasi-Gorenstein ring and we investigate when is generically quasi-Gorenstein. In addition, it is shown that is Approximately Cohen-Macaulay if and only if R is Approximately Cohen-Macaulay, provided some special conditions. Finally it is shown that if R is Approximately Gorenstein, then is Approximately Gorenstein.

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APA: Copy

TAVASOLI, E.. (2018). Amalgamated duplication of some special rings along an ideal. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 4(15 ), 31-38. SID. https://sid.ir/paper/257292/en

Vancouver: Copy

TAVASOLI E.. Amalgamated duplication of some special rings along an ideal. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;4(15 ):31-38. Available from: https://sid.ir/paper/257292/en

IEEE: Copy

E. TAVASOLI, “Amalgamated duplication of some special rings along an ideal,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 4, no. 15 , pp. 31–38, 2018, [Online]. Available: https://sid.ir/paper/257292/en

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