Soft Computing

, Volume 21, Issue 10, pp 2507–2512 | Cite as

An extension of a Y. C. Yang theorem



The main purpose of this paper is to extend the theorem of Y. C. Yang stating that lattice-ordered skew fields are totally ordered iff squares are positive (Yang in Am Math Mon 113(3):266–267, 2006). The principal tools are an extension of a result of Teh concerning weak l-groups (Teh in Proc Edinb Math Soc 13(1):123–124, 1962) and a connection with Benado multilattices introduced in Benado (Bul Şti Secţ Şti Mat Fiz 5:41–48, 1953); see also Benado (Czechoslov Math 5(3):308–344, 1955), Rudeanu and Vaida (J Mult-Valued Logic Soft Comput 20(3–4):265–307, 2013). Within the proofs below, the properties related to po-partial monoids or to po-semiring-like systems are stated such that to require each time only what is strictly needed for the stated result.


Manes Positive Cone Additive Structure Partial Additivity Multiplicative Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The present author is indebted to Yang for suggested improvements after a careful reading.

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.


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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsUniversity of BucharestBucharestRomania

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