Some Types of Filters in Equality Algebras | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 5، دوره 7، Special Issue on the Occasion of Banaschewski's 90th Birthday (II) - شماره پیاپی 1، مهر 2017، صفحه 33-55 اصل مقاله (790.06 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Rajabali Borzooei1؛ Fateme Zebardast2؛ Mona Aaly Kologani3 | ||
| 1Department of Mathematics, Shahid Beheshti University, Tehran, Iran. | ||
| 2Department of Mathematics, Payam e Noor University, Tehran, Iran. | ||
| 3Payam e Noor University | ||
| چکیده | ||
| Equality algebras were introduced by S. Jenei as a possible algebraic semantic for fuzzy type theory. In this paper, we introduce some types of filters such as (positive) implicative, fantastic, Boolean, and prime filters in equality algebras and we prove some results which determine the relation between these filters. We prove that the quotient equality algebra induced by an implicative filter is a Boolean algebra, by a fantastic filter is a commutative equality algebra, and by a prime filter is a chain, under suitable conditions. Finally, we show that positive implicative, implicative, and Boolean filters are equivalent on bounded commutative equality algebras. | ||
تازه های تحقیق | ||
Dedicated to Bernhard Banaschewski on the occasion of his 90th birthday | ||
| کلیدواژهها | ||
| Equality algebra؛ (positive) implicative filter؛ fantastic filter؛ Boolean filter | ||
| مراجع | ||
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