Modules over Trusses vs. Modules over Rings: Internal Direct Sums

Devi Fitri Ferdania (), Irawati and Hanni Garminia
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Devi Fitri Ferdania: Institut Teknologi Bandung
Irawati: Institut Teknologi Bandung
Hanni Garminia: Institut Teknologi Bandung

A chapter in Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, 2023, pp 171-185 from Springer

Abstract: Abstract A heap is an algebraic system that can be seen as a group where the existence of its identity element has not been specified. This notion results in the introduction of a truss as a ring-like system (and also a brace-like system). Thus one can observe the categorical construction of modules over trusses. Earlier, it has been shown that the direct sum of two non-empty Abelian heaps is isomorphic to a heap related to the direct sums of the group retracts of both heaps plus ℤ $$\mathbb {Z}$$ . Consequently, the internal direct sum of modules over trusses will have some differences to modules over rings. In this research, the definition and some characteristics of the internal direct sum of modules over trusses are constructed and contrasted with the corresponding characteristic of modules over rings.

Date: 2023
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DOI: 10.1007/978-3-031-28847-0_11

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