ℤ-Algebroid Structure of the Category of Groups ℤ_n and Its Subprealgebroids

Year 2026, Volume: 7 Issue: 1, 1 - 16, 31.01.2026

Osman Avcıoğlu

Abstract

In this study, we show that the category Z of all cyclic groups ℤ_n has a ℤ-algebroid structure. Moreover, we examine and characterize homsets of Z and see that each homset has a cyclic group structure. Furthermore, through narrowing homsets of Z, we obtain subpre-ℤ-algebroids of Z. In particular, for each positive integer t we get a different subpre-ℤ-algebroid Z_t of Z, where Z_1 = Z. As a consequence, we obtain a countably infinite set of (pre)algebroid samples for their use in future studies.

Keywords

Preadditive category , Algebroid , Ringoid , Cyclic groups

Ethical Statement

The author declares that the materials and methods used in his study do not require ethical committee and/or legal special permission.

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