Authors: Krapež, Aleksandar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Generalized linear functional equations on almost quasigroups I: Equations with at most two variables
Journal: Aequationes Mathematicae
Volume: 61
Issue: 3
First page: 255
Last page: 280
Issue Date: 1-Jan-2001
ISSN: 0001-9054
DOI: 10.1007/s000100050177
We define almost quasigroups, a new class of groupoids which generalize quasigroups, and prove several representation theorems for them, essentially reducing them to loops (see Theorems 1, 2 and 9). Some well-known theorems on quasigroups are generalized, notably the theorems of A. A. Albert (Theorems 8, 9 and 10). We also define the normal form of equations and show that every generalized linear functional equation Eq on almost quasigroups is equivalent to a system consisting of several equations with at most one variable each, and one equation in the normal form, with the same number of variables as Eq. Eventually, the general solution of the generalized linear functional equations on almost quasigroups with at most two variables is given. We plan to solve other generalized linear functional equations in subsequent papers.
Publisher: Springer Link
Project: Ministry of Sciences and Technology of the Republic of Serbia, Project 04M03

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