This paper introduces and systematically develops the theory of polyadic group rings, a higher arity generalization of classical group rings. We construct the fundamental operations of these structures, defining the m-ary addition and n-ary multiplic...
We construct positional numeral systems that work natively over nonderived polyadic
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 differ from that of the constituents, and the elements from different mult...
In this note, we first recall that the sets of all representatives of some special ordinary residue classes become
A novel original procedure of encryption/decryption based on the polyadic algebraic structures and on signal processing methods is proposed. First, we use signals with integer amplitudes to send information. Then, we use polyadic techniques to transf...
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented as block diagonal matrices (resulting in the Wedderburn decomposition), general forms of polyadic structures are g...
This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate various comp...