LINEAR Ω-ALGEBRAS
T. M. Baranovich, M S Burgin · Russian Mathematical Surveys · 1975
In this paper we give a brief account of the basic results in the theory of linear Ω-algebras. Particular attention is paid to research of recent years, and the connections of the theory of linear Ω-algebras with other parts of algebra are shown. For some special cases of linear Ω-algebras (ternary algebras, Γ-rings) only a survey of the literature is given. With the help of linear Ω-algebras new and simplified proofs of some known results in universal algebra are obtained. Various applications of linear Ω-algebras to functional analysis and differential geometry are described. A large number of open problems have been included, whose solution would apparently be of interest in the development of the theory of linear Ω-algebras.