Remarks on Blowing-Up Divisorial Ideals.
Lorenzo Robbiano (1979/1980)
Manuscripta mathematica
Enochs, Edgar E. (1988)
Portugaliae mathematica
Yoshiro Mori (1970)
Journal für die reine und angewandte Mathematik
Gabriel Picavet (1987)
Fundamenta Mathematicae
Gerhard O. Michler (1972)
Mathematische Zeitschrift
Ali Jaballah (2010)
Czechoslovak Mathematical Journal
A ring extension is said to be FO if it has only finitely many intermediate rings. is said to be FC if each chain of distinct intermediate rings in this extension is finite. We establish several necessary and sufficient conditions for the ring extension to be FO or FC together with several other finiteness conditions on the set of intermediate rings. As a corollary we show that each integrally closed ring extension with finite length chains of intermediate rings is necessarily a normal pair...
Jürgen Herzog (1978)
Mathematische Annalen
William Teter (1974)
Inventiones mathematicae
Robert B. jr. Warfield (1972)
Mathematische Zeitschrift
Efraim P. Armendariz (1977)
Mathematica Scandinavica
Constantin Niţă (1975)
Rendiconti del Seminario Matematico della Università di Padova
Crivei, Iuliu (2005)
International Journal of Mathematics and Mathematical Sciences
Antonio G. Rodicio (1990)
Commentarii mathematici Helvetici
Ngo Viet Trung (1980)
Monatshefte für Mathematik
Torgny Svanes (1975)
Mathematische Zeitschrift
Hideyuki Matsumura (1990)
Banach Center Publications
Noômen Jarboui (1999)
Colloquium Mathematicae
We introduce and study a new class of ring extensions based on a new formula involving the heights of their primes. We compare them with the classical altitude inequality and altitude formula, and we give another characterization of locally Jaffard domains, and domains satisfying absolutely the altitude inequality (resp., the altitude formula). Then we study the extensions R ⊆ S where R satisfies the corresponding condition with respect to S (Definition 3.1). This leads to a new characterization...
Satya Mandal (1985)
Mathematische Zeitschrift
Sohrab Sohrabi Laleh, Mir Yousef Sadeghi, Mahdi Hanifi Mostaghim (2012)
Czechoslovak Mathematical Journal
Let be a commutative Noetherian ring, an ideal of , an -module and a non-negative integer. In this paper we show that the class of minimax modules includes the class of modules. The main result is that if the -module is finite (finitely generated), is -cofinite for all and is minimax then is -cofinite. As a consequence we show that if and are finite -modules and is minimax for all then the set of associated prime ideals of the generalized local cohomology module...
Ahmad Abbasi, Hajar Roshan-Shekalgourabi, Dawood Hassanzadeh-Lelekaami (2014)
Czechoslovak Mathematical Journal
Let be a commutative Noetherian ring with identity and an ideal of . It is shown that, if is a non-zero minimax -module such that for all , then the -module is -cominimax for all . In fact, is -cofinite for all . Also, we prove that for a weakly Laskerian -module , if is local and is a non-negative integer such that for all , then and are weakly Laskerian for all and all . As a consequence, the set of associated primes of is finite for all , whenever and...