THE CHARACTERIZATION OF INTERNAL DIRECT SUM ON MODULES OVER TRUSSES
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 tru...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/54930 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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