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Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 2

On orthomorphism elements in ordered algebra

Bahri TURAN
Hüma GÜRKÖK
Pages
403–408
Publication Date
2020-03-01
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Then, under the same hypotheses, it is obtained that Orthe C is an f -algebra with a unit e.

📌 3 Key Takeaways

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Objective & Hypothesis:Let C be an ordered algebra with a unit e.
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Key Findings & Data:Firstly, it is shown that if C is an ordered algebra such that Cr , the set of all regular elements of C , is a Riesz space with the principal projection property and Orthe C is topologically full with respect to Ie , then Be = Orthe C holds, where Be is the band generated by e in Cr .
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Conclusion & Impact:Then, under the same hypotheses, it is obtained that Orthe C is an f -algebra with a unit e.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ordered algebra · orthomorphism elements · orthomorphism

Abstract

Let C be an ordered algebra with a unit e. The class of orthomorphism elements Orthe C of C was introduced and studied by Alekhno in ”The order continuity in ordered algebras”. If C = L G , where G is a Dedekind complete Riesz space, this class coincides with the band Orth G of all orthomorphism operators on G. In this study, the properties of orthomorphism elements similar to properties of orthomorphism operators are obtained. Firstly, it is shown that if C is an ordered algebra such that Cr , the set of all regular elements of C , is a Riesz space with the principal projection property and Orthe C is topologically full with respect to Ie , then Be = Orthe C holds, where Be is the band generated by e in Cr . Then, under the same hypotheses, it is obtained that Orthe C is an f -algebra with a unit e.

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Cite This Article

TURAN, B., GÜRKÖK, H. (2020). On orthomorphism elements in ordered algebra. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 2, 403–408. https://ajindex.com/articles/185554

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References (6)

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