Extended local ternary rings

Double Loops and Ternary Rings

1. Let T be a ternary ring with the ternary operation T(a, b, c) and the distinguished elements 0, 1 (see [4]). On T, two loop structures can be defined by means of the binary operations a+b = T(a, 1, b) and ab=T(a, b, 0). The resulting loops are called the additive and the multiplicative loop of Ty respectively. Together with a0 = 0a = 0 they define the structure of a double loop on T, which s...

On Fuzzy Soft Right Ternary Near-Rings

The first step towards near-rings was an axiomatic research done by Dickson in 1905. In 1936, it was Zassenhaus who used the name near-ring. Many parts of the well established theory of rings are transferred to near-rings and new specific features of near-rings have been discovered. To deal with the idea of near-rings using ternary product Warud Nakkhasen and Bundit Pibaljommee have applied the...

Additive and Multiplicative Loops of Planar Ternary Rings

Operator Space Characterizations of C*-algebras and Ternary Rings

In the category of operator spaces, that is, subspaces of the bounded linear operators B(H) on a complex Hilbert space H together with the induced matricial operator norm structure, objects are equivalent if they are completely isometric, i.e., if there is a linear isomorphism between the spaces which preserves this matricial norm structure. Since operator algebras, that is, subalgebras of B(H)...

A Holomorphic Characterization of Ternary Rings of Operators