113 citations · 374 across the 71 of their papers we have counts for
5 papers · 2 filters
Polyadic rings of -adic integers
Steven Duplij
In this note we, first, recall that the sets of all representatives of some special ordinary residue classes become -rings. Second, we introduce a possible -…
Extensions of special 3-fields
Steven Duplij, Wend Werner
We investigate finite field extensions of the unital 3-field, consisting of the unit element alone, and find considerable differences to classical field theory. Furthermore, the st…
Polyadization of algebraic structures
Steven Duplij
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in…
Polyadic analog of Grothendieck group
Steven Duplij
We generalize the Grothendieck construction of the completion group for a monoid (being the starting point of the algebraic -theory) to the polyadic case, when an initial semigr…
Polyadic analogs of direct product
Steven Duplij
We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: the arity of the product can diff…