In this paper our chief aim has been to give a definition of positive and negative elements of a partially orderedn-groupG without identity, such that this definition corresponds with the ordinary one if there do exist an identity. Further on we find two necessary and sufficient conditions to conclude about the positivity of an elementa∈G by use of the querelementā ofa. The obtained results are then used to check the law of signs of a fully ordered (n, m)-ring, and to give a starting point of pseudo-valuated (n, m)-rings.
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G. Grombez, “On (n, m)-rings”. Abhandlungen aus dem mathematischen Seminar der Universität Hamburg, vol.37 (1972), 89–108.
W. Dörnte, “Untersuchungen über einen verallgemeinerten Gruppenbegriff”. Mathematische Zeitschrift,29 (1928), 1–19.
L. Fuchs, “Partially ordered algebraic systems”. Pergamon Press, Oxford, 1963.
J. Timm, “Kommutativen-gruppen”. Dissertation, Hamburg 1967.
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Crombez, G. On partially orderedn-groups. Abh.Math.Semin.Univ.Hambg. 38, 141–146 (1972). https://doi.org/10.1007/BF02996929
- Algebraic System
- Positive Element
- Natural Order
- Strict Inclusion
- Arbitrary Integer