THE CHARACTERIZATION OF INTERNAL DIRECT SUM ON MODULES OVER TRUSSES - Fitri Ferdania, Devi
A heap, defined as a set with a suitable ternary operation, is studied from the group structure point of view. By equipping the heap structure with suitable binary operation and connect it to the ternary operation of the heaps by distributive laws, one can have trusses structure. Modules over trusses are considered and their basic properties are analysed in the sense of modules over rings. With the same terminology as modules over rings, the coproduct of modules over trusses is considered. Interestingly, it is shown that the coproduct of modules over trusses has differences with coproduct of modules over rings. This phenomenon will affect the definition and properties of the internal direct sum of modules over trusses. Thus, this research will present the construction of the internal direct sum of modules over trusses and its characterization will be determined.