Let Β΅ I denote the minimal number of generators of an ideal I of a local ring R M . The Dilworth number d R = max Β΅ I I an ideal of R and Sperner number sp R = max Β΅ M i i β₯ 0 are determined in the case that R = A G , where G = Z/pZ k is an elementary abelian p-group, A zA is a principal local ring
An application of Burnside rings in elementary finite group theory
β Scribed by Andreas W.M Dress; Christian Siebeneicher; Tomoyuki Yoshida
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 780 KB
- Volume
- 91
- Category
- Article
- ISSN
- 0001-8708
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Generalizing a theorem by J. E. Olson determining the Davenport's constant of a finite abelian p-group A, we prove that if S 1 , . . . , S k are given sets of integers satisfying suitable conditions and if g 1 , . . . , g k Κ¦ A, then a nontrivial vanishing sum of the form s 1 g 1 Ο© ΠΈ ΠΈ ΠΈ Ο© s k g k ,