A universal algebra is simple if and only if it has more than one element and there are no proper homomorphisms defined upon it. In this note we study a related notion : an algebra is pseudo-simple if and only if it has more than one element and is isomorphic to all its proper (i.e., non-one-element) homomorphic images. The two concepts simplicity and pseudo-simplicity are examples of concepts ...

Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set μ, the least fuzzy ideal containing μ is constructed. The homomorphic properties of fuzzy ideals of a pseudo-BCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras in terms of fuzzy...

Based on the Buşneag’s model ([2, 3, 4]), the notion of pseudovaluations (valuations) on a BE-algebra is introduced, and a pseudometric is induced by a pseudo-valuation on BE-algebras. Related properties are investigated, and conditions for a real-valued function on a BE-algebra to be a pseudo-valuation are discussed. Using the notion of (pseudo) valuation, we show that the binary operation in ...

In this article, we show that the flatness of a nonlinear discrete-time system can be checked by computing unique sequence involutive distributions. The well-known test for static feedback linearizability is included as special case. Since computation distributions requires only solution algebraic equations, it allows an efficient implementation in computer algebra program. case positive result...

Pseudo equality algebras were initially introduced by Jenei and Kóródi as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvurečenskij and Zahiri under the name of JK-algebras. The aim of this paper is to investigate the internal states and the state-morphisms on pseudo equality algebras. We define and study new classes of pseudo equality algebras, such as com...

Residuated lattices form the algebraic counterpart of substructural logics [4]. Rotation construction for t-norms has been introduced in [9] and has been generalized to arbitrary residuated posets in [7]. The reader is referred also to [13, 6, 5]. The rotationannihilation construction has been introduced in [10, 7]. The rotation construction has proved fundamental in the structural description ...

The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears...

Hyperoctahedral homology is the theory associated to hyperoctahedral crossed simplicial group. It defined for involutive algebras over a commutative ring using functor and bar construction of Fiedorowicz. The main result paper proves that related equivariant stable homotopy theory: discrete group odd order, algebra isomorphic fixed points under involution an infinite loop space built from class...

Some new properties of fuzzy associative filters (also known as fuzzy associative pseudo-filters), fuzzy p-filter (also known as fuzzy pseudo-p-filters), and fuzzy a-filter (also known as fuzzy pseudo-a-filters) in pseudo-BCI algebras are investigated. By these properties, the following important results are proved: (1) a fuzzy filter (also known as fuzzy pseudo-filters) of a pseudo-BCI algebra...

Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set μ, the least fuzzy ideal containing μ is constructed. The homomorphic properties of fuzzy ideals of a pseudoBCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras via fuzzy ideals a...