Ideals in (Z⁺, ≤D)
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 s...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2013 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152313 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Ideals in (Z⁺, ≤D) / S. Sagi // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 1. — С. 107–115. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862575758381154304 |
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| author | Sagi, S. |
| author_facet | Sagi, S. |
| citation_txt | Ideals in (Z⁺, ≤D) / S. Sagi // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 1. — С. 107–115. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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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| first_indexed | 2025-11-26T13:23:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152313 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-26T13:23:00Z |
| publishDate | 2013 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Sagi, S. 2019-06-09T17:20:35Z 2019-06-09T17:20:35Z 2013 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. https://nasplib.isofts.kiev.ua/handle/123456789/152313 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Ideals in (Z⁺, ≤D) Article published earlier |
| spellingShingle | Ideals in (Z⁺, ≤D) Sagi, S. |
| title | Ideals in (Z⁺, ≤D) |
| title_full | Ideals in (Z⁺, ≤D) |
| title_fullStr | Ideals in (Z⁺, ≤D) |
| title_full_unstemmed | Ideals in (Z⁺, ≤D) |
| title_short | Ideals in (Z⁺, ≤D) |
| title_sort | ideals in (z⁺, ≤d) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152313 |
| work_keys_str_mv | AT sagis idealsinzd |