Modules Over Trusses vs Modules Over Rings: Direct Sums and Free Modules
| Autor: | Bernard Rybołowicz, Tomasz Brzeziński |
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| Rok vydání: | 2020 |
| Předmět: |
Ring (mathematics)
Pure mathematics Direct sum Group (mathematics) General Mathematics 010102 general mathematics 0211 other engineering and technologies Coproduct Truss 021107 urban & regional planning 02 engineering and technology Computer Science::Numerical Analysis 01 natural sciences Physics::Space Physics Computer Science::Programming Languages Finitely-generated abelian group 0101 mathematics Abelian group Heap (data structure) Mathematics |
| Zdroj: | Algebras and Representation Theory. 25:1-23 |
| ISSN: | 1572-9079 1386-923X |
| DOI: | 10.1007/s10468-020-10008-8 |
| Popis: | Categorical constructions on heaps and modules over trusses are considered and contrasted with the corresponding constructions on groups and rings. These include explicit description of free heaps and free Abelian heaps, coproducts or direct sums of Abelian heaps and modules over trusses, and description and analysis of free modules over trusses. It is shown that the direct sum of two non-empty Abelian heaps is always infinite and isomorphic to the heap associated to the direct sum of the group retracts of both heaps and $\mathbb {Z}$ . Direct sum is used to extend a given truss to a ring-type truss or a unital truss (or both). Free modules are constructed as direct sums of a truss with itself. It is shown that only free rank-one module over a ring are free as modules over the associated truss. On the other hand, if a (finitely generated) module over a truss associated to a ring is free, then so is the corresponding quotient-by-absorbers module over this ring. |
| Databáze: | OpenAIRE |
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