Ideals in (Z⁺, ≤D)
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Ideals in (Z⁺, ≤D)
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| Creator |
Sagi, S.
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| Description |
A convolution is a mapping C of the set Z⁺ of positive integers into the set P(Z⁺) of all subsets of Z⁺ such that every member of C(n) is a divisor of n. If for any n, D(n) is the set of all positive divisors of n, then D is called the Dirichlet's convolution. It is well known that Z⁺ has the structure of a distributive lattice with respect to the division order. Corresponding to any general convolution C, one can define a binary relation ≤C on Z⁺ by 'm ≤ C n if and only if m ∈ C(n) '. A general convolution may not induce a lattice on Z⁺. However most of the convolutions induce a meet semi lattice structure on Z⁺. In this paper we consider a general meet semi lattice and study it's ideals and extend these to (Z⁺, ≤D), where D is the Dirichlet's convolution.
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| Date |
2019-06-09T17:20:35Z
2019-06-09T17:20:35Z 2013 |
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| Type |
Article
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| Identifier |
Ideals in (Z⁺, ≤D) / S. Sagi // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 1. — С. 107–115. — Бібліогр.: 9 назв. — англ.
1726-3255 2010 MSC:06B10,11A99. http://dspace.nbuv.gov.ua/handle/123456789/152313 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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