Tensor product of partially-additive monoids
type: Item
instance of: scholarly article
title: Tensor product of partially-additive monoids
zbMATH Open document ID: 0564.18007
DOI: 10.1007/BF02575521
author: Antonio Bahamonde
published in: Semigroup Forum
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134765
review text: Partially-additive monoids (pams) were introduced by Arbib and Manes in order to provide an algebraic semantics for programming languages. In this paper, we prove that the category \({\mathcal P}am\) of pams and additive maps is a closed category whose monoids are partially-additive semirings. We follow the tensor product construction of \textit{R. Guitart} [Cah. Topologie Géom. Différ. 21, 5-62 (1980; Zbl 0477.18007)] for categories of algebras which generalize the case of modules. Nevertheless, the problem here is more difficult owing to the fact that pams are partial algebras rather than algebras. Thus, we have to make some modifications to Guitart's approach.
Mathematics Subject Classification ID: 18B20
Mathematics Subject Classification ID: 68Q55
Mathematics Subject Classification ID: 18C15
Mathematics Subject Classification ID: 18D15
zbMATH DE Number: 3899133
zbMATH Keywords: Partially-additive monoids
zbMATH Keywords: algebraic semantics
zbMATH Keywords: programming languages
zbMATH Keywords: closed category
zbMATH Keywords: semirings
zbMATH Keywords: tensor product
MaRDI profile type: Publication
cites work: Q3049836
cites work: The Pattern-of-Calls Expansion Is the Canonical Fixpoint for Recursive Definitions
cites work: Can programming be liberated from the von Neumann style?
cites work: Q3704056
cites work: Tensor products of semilattices and distributive lattices
cites work: Q3934678
cites work: Q4693151
cites work: Q4123496
cites work: The inverse semigroup of a sum-ordered semiring
description: scientific article; zbMATH DE number 3899133