Characterization of regular convolutions
A convolution is a mapping \(\mathcal{C}\) of the set \(Z^{+}\) of positive integers into the set \({\mathscr{P}}(Z^{+})\) of all subsets of \(Z^{+}\) such that, for any \(n\in Z^{+}\), each member of \(\mathcal{C}(n)\) is a divisor of \(n\). If \(\mathcal{D}(n)\) is the set of all divisors of \(n\)...
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-802018-05-17T07:54:05Z Characterization of regular convolutions Sagi, Sankar semilattice, lattice, convolution, multiplicative, co-maximal, prime filter, cover, regular convolution 06B10,11A99 A convolution is a mapping \(\mathcal{C}\) of the set \(Z^{+}\) of positive integers into the set \({\mathscr{P}}(Z^{+})\) of all subsets of \(Z^{+}\) such that, for any \(n\in Z^{+}\), each member of \(\mathcal{C}(n)\) is a divisor of \(n\). If \(\mathcal{D}(n)\) is the set of all divisors of \(n\), for any \(n\), then \(\mathcal{D}\) is called the Dirichlet's convolution [2]. If \(\mathcal{U}(n)\) is the set of all Unitary(square free) divisors of \(n\), for any \(n\), then \(\mathcal{U}\) is called unitary(square free) convolution. Corresponding to any general convolution \(\mathcal{C}\), we can define a binary relation \(\leq_{\mathcal{C}}\) on \(Z^{+}\) by `\(m\leq_{\mathcal{C}}n\) if and only if \( m\in \mathcal{C}(n)\)'. In this paper, we present a characterization of regular convolution. Lugansk National Taras Shevchenko University 2018-04-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/80 Algebra and Discrete Mathematics; Vol 25, No 1 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/80/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/80/119 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/80/120 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-05-17T07:54:05Z |
| collection |
OJS |
| language |
English |
| topic |
semilattice lattice convolution multiplicative co-maximal prime filter cover regular convolution 06B10,11A99 |
| spellingShingle |
semilattice lattice convolution multiplicative co-maximal prime filter cover regular convolution 06B10,11A99 Sagi, Sankar Characterization of regular convolutions |
| topic_facet |
semilattice lattice convolution multiplicative co-maximal prime filter cover regular convolution 06B10,11A99 |
| format |
Article |
| author |
Sagi, Sankar |
| author_facet |
Sagi, Sankar |
| author_sort |
Sagi, Sankar |
| title |
Characterization of regular convolutions |
| title_short |
Characterization of regular convolutions |
| title_full |
Characterization of regular convolutions |
| title_fullStr |
Characterization of regular convolutions |
| title_full_unstemmed |
Characterization of regular convolutions |
| title_sort |
characterization of regular convolutions |
| description |
A convolution is a mapping \(\mathcal{C}\) of the set \(Z^{+}\) of positive integers into the set \({\mathscr{P}}(Z^{+})\) of all subsets of \(Z^{+}\) such that, for any \(n\in Z^{+}\), each member of \(\mathcal{C}(n)\) is a divisor of \(n\). If \(\mathcal{D}(n)\) is the set of all divisors of \(n\), for any \(n\), then \(\mathcal{D}\) is called the Dirichlet's convolution [2]. If \(\mathcal{U}(n)\) is the set of all Unitary(square free) divisors of \(n\), for any \(n\), then \(\mathcal{U}\) is called unitary(square free) convolution. Corresponding to any general convolution \(\mathcal{C}\), we can define a binary relation \(\leq_{\mathcal{C}}\) on \(Z^{+}\) by `\(m\leq_{\mathcal{C}}n\) if and only if \( m\in \mathcal{C}(n)\)'. In this paper, we present a characterization of regular convolution. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/80 |
| work_keys_str_mv |
AT sagisankar characterizationofregularconvolutions |
| first_indexed |
2025-07-17T10:31:35Z |
| last_indexed |
2025-07-17T10:31:35Z |
| _version_ |
1837890139650523136 |