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Wojciechowski, P.J. and Kreinovich, V. (1997) On Lattice Extensions of Partial Orders of Rings. Communications in Algebra, 25, 935-941.
https://doi.org/10.1080/00927879708825898

has been cited by the following article:

• TITLE: Some Results on Partially Ordered Rings

  AUTHORS: Jingjing Ma

  KEYWORDS: Algebraic, Archimedean, Infinite Prime, Integral Domain, Maximal Partial Order, Negative Square, Symmetric Partial Order, Total Order

  JOURNAL NAME: Advances in Pure Mathematics, Vol.15 No.12, December 23, 2025

  ABSTRACT: The paper presents some results on partially ordered rings. In section 2, it is shown that Archimedean directed maximal partial orders on integral domains must be total orders. Section 3 presents a direct proof that fields not algebraic over ℚ admit directed partial orders. Section 4 mainly considers the connection between symmetric partial orders, directed maximal partial orders and full infinite primes for commutative rings that are algebraic over ℤ . In particular, it is shown that in commutative rings that are algebraic over ℤ and do not contain nonzero nilpotent elements, the symmetric partial orders and full infinite primes are in one-to-one correspondence.