Abstract In this paper, in the spirit of [4], we study a new type of filters in residuated lattices : Gődel filters. So, we characterize the filters for which the quotient algebra that is constructed via these filters is a Gődel algebra and we establish the connections between these filters and other types of filters. Using Gődel filters we characterize the residuated lattices which are Gődel algebras. Also, we prove that a residuated lattice is a Gődel algebra (divisible residuated lattice, MTL algebra, BL algebra) if and only if every filter is a Gődel filter (divisible filter, MTL filter, BL filter). Finally, we present some results about injective Gődel algebras showing that complete Boolean algebras are injective objects in the category of Gődel algebras.

Dana Piciu

Christina Theresia Dan

Anca Dina

Analele Universităţii "Ovidius" Constanţa. Seria Matematică

该杂志由 MIRELA STEFANESCU 和 SILVIU SBURLAN 于 1993 年创立，致力于纯数学和应用数学。由罗马尼亚康斯坦察奥维迪乌斯大学数学和计算机科学学院出版。

The journal "Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica" was founded in 1993 by MIRELA STEFANESCU and SILVIU SBURLAN, focusing on research in pure and applied mathematics. It is published by the Faculty of Mathematics and Computer Science at Ovidius University in Constanta, Romania.

《Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica》杂志由MIRELA STEFANESCU和SILVIU SBURLAN于1993年创立，专注于纯数学和应用数学的研究。该杂志由罗马尼亚康斯坦察的奥维迪乌斯大学数学与计算机科学学院出版。

Category	Quartile
数学	4
数学, 数学	4
数学, 应用数学	4

Gődel filters in residuated lattices

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Journal Info

Category	Quartile
MATHEMATICS, APPLIED	3