In this paper the notion of fuzzy dot BCK-subalgebra is introduced. We state and prove some theorem in fuzzy dot BCK-subalgebra and level subalgebras. Mathematics Subject Classification: 06F35, 03G25, 94D05

This paper deals with some properties of n-fold commutative ideals and n-fold weak commutative ideals in BCK-algebras. Afterwards, we construct some algorithms for studying foldness theory of commutative ideals in BCK-algebras.

We investigate quantitative properties of BCI and BCK logics. The first part of the paper compares the number of formulas provable in BCI versus BCK logics. We consider formulas built on implication and a fixed set of k variables. We investigate the proportion between the number of such formulas of a given length n provable in BCI logic against the number of formulas of length n provable in ric...

Several types of skeletons in a hyper MV-algebra are introduced, and their relations are investigated.

We study infinitesimal deformations of autodual and hyper-holomorphic connections on complex vector bundles hyper-Kähler manifolds arbitrary dimension. In particular, we describe the DG Lie algebra controlling this deformation problem. Moreover, prove associative formality for derived endomorphisms a holomorphic bundle admitting projectively connection.

This paper presents some methods of representing canonical commutation relations in terms of hyper nite-dimensional matrices, which are constructed by nonstandard analysis. The rst method uses representations of a nonstandard extension of nite Heisenberg group, called hyper nite Heisenberg group. The second is based on hyper nite-dimensional representations of so(3). Then, the cases of in nite ...

BCK-algebras, introduced in the 1960s by Imai and Iséki [3], form a well-known class of algebras intensively studied in algebraic logic during the last decades. The reason of their introduction was practically twofold: they describe general properties of algebras of sets with the set subtraction as a binary operation, and secondly, they form a natural generalization of algebraic counterparts of...

if we formulate our logics in a Gentzen-type formal system. Some syntactical properties of these logics have been studied firstly by the second author in [I I], in connection with the study of BCK-algebras (for information on BCK-algebras, see [9]). There, it turned out that such a syntactical method is a powerful and promising tool in studying BCK-algebras. Using this method, considerable prog...

The main purpose of the paper is to study hyperkähler structures from the viewpoint of symplectic geometry. We introduce a notion of hypersymplectic structures which encompasses that of hyperkähler structures. Motivated by the work of Kronheimer on (co)adjoint orbits of semi-simple Lie algebras [10] [11], we define hyper-Lie Poisson structures associated with a compact semi-simple Lie algebra a...