Positive implicative ordered filters of implicative semigroups
We introduce the notion of positive implicative ordered filters in implicative semigroups. We show that every positive implicative ordered filter is both an ordered filter and an implicative ordered filter. We give examples that an ordered filter (an implicative ordered filter) may not be a positive...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200003781 |
| Summary: | We introduce the notion of positive implicative ordered filters in
implicative semigroups. We show that every positive implicative
ordered filter is both an ordered filter and an implicative ordered
filter. We give examples that an ordered filter (an implicative
ordered filter) may not be a positive implicative ordered filter.
We also give equivalent conditions of positive implicative ordered
filters. Finally we establish the extension property for positive
implicative ordered filters. |
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| ISSN: | 0161-1712 1687-0425 |