Relatively orthocomplemented skew nearlattices in Rickart rings

Cırulis, J.

Artykuł - szczegóły

Tytuł artykułu

Relatively orthocomplemented skew nearlattices in Rickart rings

Autorzy

Cırulis J.

Wybrane pełne teksty z tego czasopisma

http://www.degruyter.com/view/j/dema

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Warianty tytułu

Konferencja

Proceedings of the AAA88 - 88th Workshop on General Algebra Editors for the Special Issue: Anna Romanowska, Jonathan D. H. Smith

Języki publikacji

Abstrakty

A class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤; such bands are known as right normal skew nearlattices. The poset (R, ≤) is relatively orthocomplemented; in particular, every initial segment in it is orthomodular. The order ≤ is actually a version of the so called right-star order. The one-sided star orders are well-investigated for matrices and recently have been generalized to bounded linear Hilbert space operators and to abstract Rickart *-rings. The paper demonstrates that they can successfully be treated also in Rickart rings without involution.

Słowa kluczowe

orthogonality relatively orthocomplemented poset restrictive semigroup Rickart ring right normal band right-star order skew nearlattice

ortogonalność poset półgrupa restrykcyjna pierścień Rickarta pas półgrupa

Wydawca

De Gruyter

Czasopismo

Demonstratio Mathematica

Rocznik

2015

Tom

Vol. 48, nr 4

Strony

493--508

Opis fizyczny

Bibliogr. 20 poz.

Twórcy

autor

Cırulis J.

jc@lanet.lv

Institute of Mathematics and Computer Science, University of Latvia, Raina b., 29 Riga, LV-1459, Latvia

Bibliografia

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[5] J. Cīrulis, Skew nearlattices: some structure and representation theorems, in: I. Chajda et al. (eds.), Contributions to General Algebra 19, Verlag Johannes Heyn, Klagenfurt, 2010, 33–44.
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[7] J. Cīrulis, Lattice operators on Rickart *-rings under the star order, Linear Multilinear Algebra 63 (2015), 497–708, DOI 10.1080/03081087.2013.873429.
[8] J. Cīrulis, On one-sided star partial orders on a Rickart *-ring, arXiv:1410.4693v1, 2014.
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Typ dokumentu

Bibliografia

Identyfikator YADDA

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