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A complete structure theorem of Sally modules of m-primary ideals I in a Cohen-Macaulay local ring (A,m) satisfying the equality e1(I) = e0(I)−lA(A/I)+1 is given, where e0(I) and e1(I) denote the first two Hilbert coefficients of I.

- Luca Luigi Ghezzi, Shiro Goto, J. Hong, Kazuho Ozeki, Thien Thuong Phuong, Wolmer V. Vasconcelos
- 2010

The conjecture of Wolmer Vasconcelos on the vanishing of the first Hilbert coefficient e1(Q) is solved affirmatively, where Q is a parameter ideal in a Noetherian local ring. Basic properties of the rings for which e1(Q) vanishes are derived. The invariance of e1(Q) for parameter ideals Q and its relationship to Buchsbaum rings are studied.

The structure of Sally modules of m-primary ideals I in a CohenMacaulay local ring (A,m) satisfying the equality e1(I) = e0(I) − lA(A/I) + 1 is explored, where e0(I) and e1(I) denote the first two Hilbert coefficients of I.

- Kazuho Ozeki
- 2009

A complete structure theorem of Sally modules of m-primary ideals I in a Cohen-Macaulay local ring (A,m) satisfying the equality e1(I) = e0(I)− `A(A/I) + 1 is given, where e0(I) and e1(I) denote the first two Hilbert coefficients of I.

- Shiro Goto, Kazuho Ozeki, +4 authors Ryo Takahashi
- 2012

In this paper we study Ulrich ideals of and Ulrich modules over Cohen–Macaulay local rings from various points of view. We determine the structure of minimal free resolutions of Ulrich modules and their associated graded modules, and classify Ulrich ideals of numerical semigroup rings and rings of finite CM-representation type.

- Teruaki Aizawa, Terumasa Ebara, Kazuho Ozeki
- Kybernetik
- 1974

- Shiro Goto, Kazuho Ozeki, +4 authors Ryo Takahashi
- 2014

In this paper we study Ulrich ideals of and Ulrich modules over Cohen–Macaulay local rings from various points of view. We determine the structure of minimal free resolutions of Ulrich modules and their associated graded modules, and classify Ulrich ideals of numerical semigroup rings and rings of finite CM-representation type.

- Teruaki Aizawa, Terumasa Ebara, Kazuho Ozeki, Yoshinori Uesaka
- Kybernetik
- 2004

There have been two contrasting doctrines concerning learning, more generally about acquisition of knowledge: empiricism and rationalism. The theory of learning in such a field as artificial intelligence seems to fall within the empiricist framework. On the hand, N. Chomsky and his followers have discussed, during the last decade, concerning learning,… (More)

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