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Vague ideals of implication groupoids

Ravi Kumar Bandaru, K.P. Shum (2013)

Discussiones Mathematicae - General Algebra and Applications

We introduce the concept of vague ideals in a distributive implication groupoid and investigate their properties. The vague ideals of a distributive implication groupoid are also characterized.

Varieties of Distributive Rotational Lattices

Gábor Czédli, Ildikó V. Nagy (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A rotational lattice is a structure L ; , , g where L = L ; , is a lattice and g is a lattice automorphism of finite order. We describe the subdirectly irreducible distributive rotational lattices. Using Jónsson’s lemma, this leads to a description of all varieties of distributive rotational lattices.

Very true operators on MTL-algebras

Jun Tao Wang, Xiao Long Xin, Arsham Borumand Saeid (2016)

Open Mathematics

The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized...

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