On the cancellation problem for quantales
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Published:2022-10-13
Issue:
Volume:
Page:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Wu Hongwei1,
Zhao Bin1ORCID
Affiliation:
1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119, P. R. China
Abstract
In this paper, we consider the cancellation problem for direct products in the category of quantales. It is easy to see that quantales are not always cancelable. We show that indecomposable quantales, simple quantales, quantales without zero-divisors and quantales without nontrivial idempotent elements except the top element are cancelable. We also prove that each quantale can be embedded into a (unital) cancelable quantale.
Funder
National Natural Science Foundation of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
1 articles.
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