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Amalgamated duplication of some special rings along an ideal | ||
Journal of New Researches in Mathematics | ||
مقاله 3، دوره 4، شماره 15، بهمن 2018، صفحه 31-38 اصل مقاله (318.62 K) | ||
نوع مقاله: research paper | ||
نویسنده | ||
E. Tavasoli | ||
Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Extension of ring along an ideal؛ Generically Gorenstein؛ Generically Cohen-Macaulay؛ Approximately Gorenstein؛ Approximately Cohen-Macaulay | ||
آمار تعداد مشاهده مقاله: 249 تعداد دریافت فایل اصل مقاله: 374 |