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Constructing new Segal topological algebras from existing ones.

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Title: Constructing new Segal topological algebras from existing ones.
Alternate Title: Uute Segali topoloogiliste algebrate konstrueerimine olemasolevatest.
Authors: Piik, René1 rene.piik@ut.ee, Abel, Mart2,3
Source: Proceedings of the Estonian Academy of Sciences. 2025, Vol. 74 Issue 4, p539-543. 5p.
Subjects: Topological algebras, Vector spaces, Mathematics, Ordered algebraic structures
Abstract (English): In this paper, we examine the properties of Segal topological algebras, looking at ways to construct new objects from existing ones. Equipped with the example of algebras (in the sense of vector spaces equipped with multiplication), we consider two approaches: one via a direct product of an arbitrary family of Segal topological algebras and another using the Dorroh extensions of the underlying topological algebras. [ABSTRACT FROM AUTHOR]
Abstract (Estonian): Artiklis esitatakse kaks viisi olemasolevatest Segali topoloogilistest algebratest uute konstrueerimiseks. Esmalt näidatakse, et Segali topoloogiliste algebrate peal töötab ning on kooskõlas neil antud topoloogiatega tavaline otsekorrutise konstruktsioon. Seejärel tõestatakse, et pea kõiki Segali topoloogilisi algebraid on võimalik ühikustada, lähtudes topoloogilisse algebrasse Dorroh' laiendi abil ühikelemendi juurdetoomisest. Ainsaks (tarvilikuks ja piisavaks) tingimuseks osutub, et Segali topoloogilist algebrat määrav homomorfism peab olema sürjektiivne. [ABSTRACT FROM AUTHOR]
Copyright of Proceedings of the Estonian Academy of Sciences is the property of Teaduste Akadeemia Kirjastus and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Constructing new Segal topological algebras from existing ones.
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  Data: Uute Segali topoloogiliste algebrate konstrueerimine olemasolevatest.
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  Data: <searchLink fieldCode="AR" term="%22Piik%2C+René%22">Piik, René</searchLink><relatesTo>1</relatesTo><i> rene.piik@ut.ee</i><br /><searchLink fieldCode="AR" term="%22Abel%2C+Mart%22">Abel, Mart</searchLink><relatesTo>2,3</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+Estonian+Academy+of+Sciences%22">Proceedings of the Estonian Academy of Sciences</searchLink>. 2025, Vol. 74 Issue 4, p539-543. 5p.
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  Data: <searchLink fieldCode="DE" term="%22Topological+algebras%22">Topological algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+spaces%22">Vector spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Ordered+algebraic+structures%22">Ordered algebraic structures</searchLink>
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  Label: Abstract (English)
  Group: Ab
  Data: In this paper, we examine the properties of Segal topological algebras, looking at ways to construct new objects from existing ones. Equipped with the example of algebras (in the sense of vector spaces equipped with multiplication), we consider two approaches: one via a direct product of an arbitrary family of Segal topological algebras and another using the Dorroh extensions of the underlying topological algebras. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label: Abstract (Estonian)
  Group: Ab
  Data: Artiklis esitatakse kaks viisi olemasolevatest Segali topoloogilistest algebratest uute konstrueerimiseks. Esmalt näidatakse, et Segali topoloogiliste algebrate peal töötab ning on kooskõlas neil antud topoloogiatega tavaline otsekorrutise konstruktsioon. Seejärel tõestatakse, et pea kõiki Segali topoloogilisi algebraid on võimalik ühikustada, lähtudes topoloogilisse algebrasse Dorroh' laiendi abil ühikelemendi juurdetoomisest. Ainsaks (tarvilikuks ja piisavaks) tingimuseks osutub, et Segali topoloogilist algebrat määrav homomorfism peab olema sürjektiivne. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Proceedings of the Estonian Academy of Sciences is the property of Teaduste Akadeemia Kirjastus and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3176/proc.2025.4.07
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      – Code: eng
        Text: English
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        StartPage: 539
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      – SubjectFull: Topological algebras
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      – SubjectFull: Vector spaces
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      – SubjectFull: Mathematics
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      – TitleFull: Constructing new Segal topological algebras from existing ones.
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              M: 10
              Text: 2025
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