On orthomorphism elements in ordered algebra

Bahri TURAN; Hüma GÜRKÖK

doi:https://doi.org/10.3906/mat-1911-28

Makale detayları

On orthomorphism elements in ordered algebra

Yazarlar:

Bahri TURAN | Hüma GÜRKÖK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2020 Vol.44 Issue 2, pp.403-408

Belge Tipi:

Makale

Yayın Tarihi:

2/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000745450

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

DOI:

https://doi.org/10.3906/mat-1911-28

Özet:

 

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.

Makale detayları

On orthomorphism elements in ordered algebra

Yazarlar: Bahri TURAN | Hüma GÜRKÖK

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2020 Vol.44 Issue 2, pp.403-408

Belge Tipi: Makale

Yayın Tarihi: 2/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000745450

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

DOI: https://doi.org/10.3906/mat-1911-28

Sayı

Yazarlar:

Bahri TURAN | Hüma GÜRKÖK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2020 Vol.44 Issue 2, pp.403-408

Belge Tipi:

Makale

Yayın Tarihi:

2/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000745450

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

DOI:

https://doi.org/10.3906/mat-1911-28