### The Arithmetic of Generalization for General Products of Monoids

#### Abstract

For \(A\) and \(B\) arbitrary monoids. In a recent work, Cevik *et al.* (*Hacettepe Journal of Mathematics and Statistics* **50**(1) (2021), 224 - 234) defined new consequence of the general product denoted by \(A^{\oplus B}_{\delta

}\bowtie _{\psi }B^{\oplus A}\) and gave a presentation for this generalization. In this paper, we explore the way in which the structure of the generalization of general product reflects the properties of its associated wreath products.

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DOI: http://dx.doi.org/10.26713%2Fcma.v12i1.1412

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