The determinant is a main organizing tool in commutative linear algebra. In this review we present a theory of the quasideterminants defined for matrices over a division algebra. We believe that the notion of quasideterminants should be a main organizing tool in noncommutative algebra giving them the same role determinants play in commutative algebra.

Processing of the certain information, especially inferences based on certain information. Is based on classical two-valued logic. Due to strict and complete logical foundation (classical logic), making inference levels. Thus, it is natural and necessary to attempt to establish some rational logic system as the logical foundation for uncertain information processing. It is evident that this kin...

BCK and BCI-algebras, two classes of algebras of logic, were introduced by Imai and Iseki [1], Iseki [2] and Iseki and Tanaka [3] and have been extensively studied by various other researchers [4, 5]. It is known that the class of BCK-algebras is a proper subclass of the class of BCI-algebras. In [6, 7] a wider class of abstract algebras was introduced by Q.P.Hu and X.Li.They have shown that th...

This talk will provide a snapshot of contemporary commutative algebra. In classical commutative algebra and algebraic number theory, the Dedekind domains are the most important class of rings. Modern commutative algebra studies numerous generalizations of the Dedekind domains in attempts to generalize results of algebraic number theory. This talk will introduce a few important generalizations o...

We show that the complexification (Ã, τ̃) of a real locally pseudoconvex (locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra (A,τ) is a complex locally pseudoconvex (resp., locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra and all elements in the complexification (Ã, τ̃) of a commutati...

We describe geometric non-commutative formal groups in terms of a geometric commutative formal group with a Poisson structure on its splay algebra. We describe certain natural properties of such Poisson structures and show that any such Poisson structure gives rise to a non-commutative formal group. We describe geometric non-commutative formal groups in terms of a geometric commutative formal g...