The motivation of this article is to define approximately near rings, some types $N$-groups, ideals, and rings all descriptive cosets. Moreover, properties these algebraic structures are given. Furthermore, near-ring homomorphisms introduced their investigated.

We consider some families of one relator groups arising as fundamental 3-dimensional manifolds, and calculate their character varieties in SL(2, C). Then we give simple geometrical descriptions such varieties, determine the number irreducible components. Our paper relates to work Baker-Petersen, Qazaqzeh Morales-Marcén on variety certain classes groups, but use different methods based concept p...

A well-known conjecture says that every one-relator group is coherent. We state and partly prove a similar statement for graded associative algebras. In particular, we show that every Gorenstein algebra A of global dimension 2 is graded coherent. This allows us to define a noncommutative analogue of the projective line P as a noncommutative scheme based on the coherent noncommutative spectrum q...

Motivated by algorithmic problems from combinatorial group theory we study computational properties of integers equipped with binary operations +, −, z = x2, z = x2 (the former two are partial) and predicates < and =. Notice that in this case very large numbers, which are obtained as n towers of exponentiation in the base 2 can be realized as n applications of the operation x2, so working with ...