Mathematical Journal of Ibaraki University

Mathematical Journal of Ibaraki University

Online ISSN : 1883-4353
Print ISSN : 1343-3636
ISSN-L : 1343-3636

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Volume 49

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A gg-cancellative semistar operation on an integral domain need not be gh-cancellative; Addendum

Ryûki Matsuda

2017 Volume 49 Pages 1-10
Published: 2017
Released on J-STAGE: September 15, 2017

DOIhttps://doi.org/10.5036/mjiu.49.1

JOURNAL FREE ACCESS

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This is an addendum to our [5]. In this paper, we introduce rational Euclidean spaces, and study them. It is shown that they are connected with the valuations on the integral domain in [5].

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Some results on presemistar operations

Akira Okabe

2017 Volume 49 Pages 11-22
Published: 2017
Released on J-STAGE: September 15, 2017

DOIhttps://doi.org/10.5036/mjiu.49.11

JOURNAL FREE ACCESS

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In [O3], we introduced the notion of presemistar operation as a generalization of the notion of semistar operation and gave some characterizations of presemistar operations. In this paper we shall give some new characterizations of presemistar operations. We also introduced the notion of an s.e.a.b. presemistar operation in [O3]. One of the main results of this paper is to show that there exists an example of a proper presemistar operation which is e.a.b. but is not s.e.a.b.. We also give two methods of construction which will provide many new examples of presemistar operations.

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