Results 1 to 10 of about 194,411 (117)
F-Rationality of Rees Algebras [PDF]
Journal of Algebra, 2002 Many authors have studied various properties of Rees algebras; this paper is the first systematic study of the F-rationality: Under what conditions on the ring \(R\) and on the ideal \(I\) does the F-rationality of \(R\) imply the F-rationality of the Rees algebra \(R(I)\), and vice versa? One of the techniques the authors employ is the Sancho de Salas
Kei-Ichi Watanabe +2 more
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Rees Algebras of F-regular Type [PDF]
Journal of Algebra, 2002 A reduced ring \(R\) of characteristic \(p> 0\) is said to be F-regular if the map \(R\to R^{1/p}\) is module-finite and for every \(c\in R\) not in any minimal prime of \(R\), there exists a power \(q= p^e\) such that the \(R\)-linear inclusion \(c^{1/q}R\to R^{1/q}\) splits.
Kei-Ichi Watanabe +2 more
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, 2021 We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a source of challenging problems in its own right. We provide an invitation to this area of investigation by stating several open questions.
Eloisa Grifo, Alexandra Seceleanu
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Journal of Algebra, 1988 Let R be an integral domain and I an ideal of R. Let \(I_ a\) denote the integral closure of I. I is complete if \(I=I_ a\) and I is normal if each power of I is complete. It is well-known that if R is a two- dimensional regular local ring, then complete ideals are normal.
A Simis, W V Vasconcelos
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Elimination and nonlinear equations of Rees algebras
Journal of Algebra, 2010 A new approach is established to computing the image of a rational map, whereby the use of approximation complexes is complemented with a detailed analysis of the torsion of the symmetric algebra in certain degrees. In the case the map is everywhere defined this analysis provides free resolutions of graded parts of the Rees algebra of the base ideal in
Aron Simis +2 more
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F-rationality of Rees algebras [PDF]
Journal of Algebra, 2021 In this paper, we study the $F$-rationality of the Rees algebra and the extended Rees algebra of $\mathfrak{m}$-primary ideals in excellent local rings $(R, \mathfrak{m})$ of prime characteristic. We partially answer some conjectures and questions raised by N. Hara, K.-i. Watanabe and K.-i. Yoshida (J. Algebra, pp.153--190, vol 247, 2002).
Mitra Koley, Manoj Kummini
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Singularities of Rees-like algebras [PDF]
Mathematische Zeitschrift, 2020 31 ...
Mantero, Paolo +2 more
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Approximate Biprojectivity of ℓ1-Munn Banach Algebras
Journal of Mathematics, 2022 In the present paper, we study the approximate biprojectivity and weak approximate biprojectivity of ℓ1-Munn Banach algebras when the related sandwich matrix is regular over InvA.
G. Zarei +3 more
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A Family of Quotients of the Rees Algebra [PDF]
Communications in Algebra, 2014 A family of quotient rings of the Rees algebra associated to a commutative ring is studied. This family generalizes both the classical concept of idealization by Nagata and a more recent concept, the amalgamated duplication of a ring. It is shown that several properties of the rings of this family do not depend on the particular member.
Barucci V, D'ANNA, Marco, Strazzanti F.
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Fibers of rational maps and Rees algebras of their base ideals
Tạp chí Khoa học Đại học Huế: Khoa học Tự nhiên, 2020 We consider a ratinonal map $\phi$ from m-dimensional projective space to n-dimensional projective space that is a parameterization of m-dimensional variety. Our main goal is to study the (m-1)-dimensional fibers of $\phi$ in relation with the m-th local
Tran Quang Hoa, Ho Vu Ngoc Phuong
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