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… Click to show full abstract
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.
               
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