Quasideterminants Page 1 http://www.elsevier.com/locate/aim Advances in Mathematics 193
(2005) 56–141 Quasideterminants Israel Gelfand,a Sergei Gelfand,b,√ Vladimir Retakh,a,1 …

In this paper we develop a theory of slice regular functions on a real alternative algebra A.
Our approach is based on a well-known Fueter's construction. Two recent function theories …

We study the non-uniqueness of factorizations of non zero-divisors into atoms (irreducibles)
in noncommutative rings. To do so, we extend concepts from the commutative theory of non …

A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic
subset of K. Such a polynomial is always a product of linear factors over K, although not …

We introduce and study" isomonodromy" transformations of the matrix linear difference
equation Y (z+ 1)= A (z) Y (z) with polynomial A (z). Our main result is construction of an …

We expose the main results of a theory of slice regular functions on a real alternative
algebra A, based on a well-known Fueter construction. Our general theory includes the …

A polynomial f (t) in an Ore extension K [t; S, D] over a division ring K is a Wedderburn
polynomial if f (t) is monic and is the minimal poly-nomial of an algebraic subset of K. These …

We study in detail the zero set of a slice regular function of a quaternionic or octonionic
variable. By means of a division lemma for convergent power series, we find the exact …

To any directed graph we associate an algebra with edges of the graph as generators and
with relations defined by all pairs of directed paths with the same origin and terminus. Such …

Let K, S, D be a division ring, an endomorphism and a S-derivation of K, respectively. In this
setting we introduce generalized noncommutative symmetric functions and obtain Viète …