Mathematical Journal of Ibaraki University

The semistar operations on certain Prüfer domain

Ryûki Matsuda

2011 Volume 43 Pages 1-12
Published: 2011
Released on J-STAGE: November 15, 2011

DOIhttps://doi.org/10.5036/mjiu.43.1

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Let D be a 1-dimensional Prüfer domain with exactly two maximal ideals. We determine the semistar operations on D.

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Caloric morphisms between different radial metrics on semi-euclidean spaces of same dimension

Katsunori Shimomura

2011 Volume 43 Pages 13-41
Published: 2011
Released on J-STAGE: November 15, 2011

DOIhttps://doi.org/10.5036/mjiu.43.13

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This paper generalizes and improves the result of [8] to caloric morphisms between manifolds with different radial semi-euclidean metrics. It is based on the similar arguments as were used in [7] and [8] (cf. [4], [5], [6]), but it succeed to remove the technical assumption from the main result of [8].

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Some results on a conjecture regarding Mori domain

Habte Gebru

2011 Volume 43 Pages 43-50
Published: 2011
Released on J-STAGE: November 15, 2011

DOIhttps://doi.org/10.5036/mjiu.43.43

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Based on the famous Mori-Nagata Theorem: The integral closure of a noetherian domain is a Krull domain, similar assertion was conjectured for Mori domain as follows: The complete integral closure of a Mori domain is a Krull domain.
The conjecture is positive for a noetherian domain, Krull domain, a semi normal Mori domain [6] and Mori domains for which (D : D^*) ≠ 0.
In general, as M. Roitman has noted [26], the conjecture is not true.
In this paper, an attempt is being made, among other things, to prove that the conjecture is true for a one dimensional Mori domain and for a finite dimensional AV- Mori domain. On the other hand, using the idea of conductor ideals, a simplified proof is given that the conjecture is true for semi normal Mori domains with nonzero pseudo radical.

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Liouville type theorem associated with the wave equation

Katsunori Shimomura

2011 Volume 43 Pages 51-64
Published: 2011
Released on J-STAGE: November 15, 2011

DOIhttps://doi.org/10.5036/mjiu.43.51

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