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Ivan Chajda, Miroslav Kolařík (2009)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
The concept of a basic pseudoring is introduced. It is shown that every orthomodular lattice can be converted into a basic pseudoring by using of the term operation called Sasaki projection. It is given a mutual relationship between basic algebras and basic pseudorings. There are characterized basic pseudorings which can be converted into othomodular lattices.
Mahdeieh Abbasloo, Arsham Borumand Saeid (2011)
Discussiones Mathematicae - General Algebra and Applications
In this paper, we introduce the notion of a bi-BL-algebra, bi-filter, bi-deductive system and bi-Boolean elements of a bi-BL-algebra and deal with bi-filters in bi-BL-algebra. We study this structure and construct the quotient of bi-BL-algebra. Also present a classification for examples of proper bi-BL-algebras.
Buşneag, Dumitru, Piciu, Dana (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Radim Bělohlávek (2003)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Jiří Rachůnek, Vladimír Slezák (2006)
Mathematica Slovaca
Ivan Chajda, Peter Emanovský (2004)
Discussiones Mathematicae - General Algebra and Applications
We introduce a bounded lattice L = (L;∧,∨,0,1), where for each p ∈ L there exists an antitone involution on the interval [p,1]. We show that there exists a binary operation · on L such that L is term equivalent to an algebra A(L) = (L;·,0) (the assigned algebra to L) and we characterize A(L) by simple axioms similar to that of Abbott's implication algebra. We define new operations ⊕ and ¬ on A(L) which satisfy some of the axioms of MV-algebra. Finally we show what properties must be satisfied by...
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