Note on gilmer’s multiplicative ideal theory, I
Source
The Arabian Journal for Science and Engineering. Section C, Theme issues
Issue
Vol. 26, Issue 1C (31 Dec. 2001), pp.127-140, 14 p.
Publisher
King Fahd University of Petroleum and Minerals
Publication Date
2001-12-31
Country of Publication
Saudi Arabia
No. of Pages
14
Main Subjects
Engineering & Technology Sciences (Multidisciplinary)
Abstract EN
As a branch of the commutative ring theory, we have the multiplicative ideal theory.
Also, Gilmer’s Multiplicative Ideal Theory [1] is a basic reference in multiplicative ideal theory.
We know that various terms in the theory are defined analogously for semigroups (especially, for commutative semigroups); those are ideal, integral element, common divisor, common multiple, (Krull) dimension, valuation.....We confer A.H.
Clifford and G.B.
Preston [2], which is a basic reference in the theory of semigroups.
The aim of this note is to prove or disprove all theorems in [ 1, Chapters I-V] for commutative semigroups (explicitly, for grading monoids).
We allow this note to be self-contained.
We leave two questions.
American Psychological Association (APA)
Matsuda, Ryuki. 2001. Note on gilmer’s multiplicative ideal theory, I. The Arabian Journal for Science and Engineering. Section C, Theme issues،Vol. 26, no. 1C, pp.127-140.
https://search.emarefa.net/detail/BIM-389490
Modern Language Association (MLA)
Matsuda, Ryuki. Note on gilmer’s multiplicative ideal theory, I. The Arabian Journal for Science and Engineering. Section C, Theme issues Vol. 26, no. 1C (Dec. 2001), pp.127-140.
https://search.emarefa.net/detail/BIM-389490
American Medical Association (AMA)
Matsuda, Ryuki. Note on gilmer’s multiplicative ideal theory, I. The Arabian Journal for Science and Engineering. Section C, Theme issues. 2001. Vol. 26, no. 1C, pp.127-140.
https://search.emarefa.net/detail/BIM-389490
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 140
Record ID
BIM-389490