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Algebra and Discrete Mathematics, 2017, том 24, выпуск 1, страницы 90–98
(Mi adm620)
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RESEARCH ARTICLE
Flat extension and phantom homology
Rajsekhar Bhattacharyya Dinabandhu Andrews College, Garia, Kolkata 700084, India
Аннотация:
Phantom homology arises in tight closure theory due to small non-exactness when ‘kernel’ is not equal to ‘image’ but ‘kernel’ is in the tight closure of the ‘image’. In this paper we study a typical flat extension, which we call $*$-flat extension, such that upon tensoring which preserves phantom homology. Along with other properties, we observe that $*$-flat extension preserves ghost regular sequence, which is a typical ‘tight closure’ generalization of regular sequence. We also show that in some situations, under $*$-flat extension, test ideal of the $*$-flat algebra is the expansion of the test ideal of the base ring.
Ключевые слова:
tight closure, phantom homology.
Поступила в редакцию: 23.09.2015 Исправленный вариант: 12.05.2016
Образец цитирования:
Rajsekhar Bhattacharyya, “Flat extension and phantom homology”, Algebra Discrete Math., 24:1 (2017), 90–98
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm620 https://www.mathnet.ru/rus/adm/v24/i1/p90
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