Weak implicative filters in quasi-ordered residuated systems
Abstract: The concept of residuated relational systems ordered under a quasiorder relation was introduced in 2018 by S. Bonzio and I. Chajda as a structure A = 〈A, ·,→, 1, R〉, where (A, ·) is a commutative monoid with the identity 1 as the top element in this ordered mo...
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2021
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oai:scielo:S0716-091720210003007972021-06-07Weak implicative filters in quasi-ordered residuated systemsRomano,Daniel A. Quasi-ordered residuated relational system Filter Implicative filter Weak implicative filter Abstract: The concept of residuated relational systems ordered under a quasiorder relation was introduced in 2018 by S. Bonzio and I. Chajda as a structure A = 〈A, ·,→, 1, R〉, where (A, ·) is a commutative monoid with the identity 1 as the top element in this ordered monoid under a quasi-order R. The author introduced and analyzed the concepts of filters and implicative filters in this type of algebraic structures. In this article, the concept of weak implicative filters in a quasi-ordered residuated system is introduced as a continuation of previous researches. Also, some conditions for a filter of such system to be a weak implicative filter are listed.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.3 20212021-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000300797en10.22199/issn.0717-6279-4332 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Quasi-ordered residuated relational system Filter Implicative filter Weak implicative filter |
| spellingShingle |
Quasi-ordered residuated relational system Filter Implicative filter Weak implicative filter Romano,Daniel A. Weak implicative filters in quasi-ordered residuated systems |
| description |
Abstract: The concept of residuated relational systems ordered under a quasiorder relation was introduced in 2018 by S. Bonzio and I. Chajda as a structure A = 〈A, ·,→, 1, R〉, where (A, ·) is a commutative monoid with the identity 1 as the top element in this ordered monoid under a quasi-order R. The author introduced and analyzed the concepts of filters and implicative filters in this type of algebraic structures. In this article, the concept of weak implicative filters in a quasi-ordered residuated system is introduced as a continuation of previous researches. Also, some conditions for a filter of such system to be a weak implicative filter are listed. |
| author |
Romano,Daniel A. |
| author_facet |
Romano,Daniel A. |
| author_sort |
Romano,Daniel A. |
| title |
Weak implicative filters in quasi-ordered residuated systems |
| title_short |
Weak implicative filters in quasi-ordered residuated systems |
| title_full |
Weak implicative filters in quasi-ordered residuated systems |
| title_fullStr |
Weak implicative filters in quasi-ordered residuated systems |
| title_full_unstemmed |
Weak implicative filters in quasi-ordered residuated systems |
| title_sort |
weak implicative filters in quasi-ordered residuated systems |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2021 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000300797 |
| work_keys_str_mv |
AT romanodaniela weakimplicativefiltersinquasiorderedresiduatedsystems |
| _version_ |
1718439906963881984 |