The main objective of this paper is the study of rings with a relation which has all the properties of an order relation on a ring except, perhaps, for one: transitivity. Consequently, many of the results presented here are generalizations of well-known facts about transitively ordered rings; and most, but not all, of the conclusions of this paper are applicable to such rings.
","abstract_html":"<p>The main objective of this paper is the study of rings with a relation which has all the properties of an order relation on a ring except, perhaps, for one: transitivity. Consequently, many of the results presented here are generalizations of well-known facts about transitively ordered rings; and most, but not all, of the conclusions of this paper are applicable to such rings.</p>","abstract_has_math":false,"creators":["Machtinger, Lawrence Arnold"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Open Access Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1965,"date_issued":"1965-05-01T07:00:00Z","date_published":"1965-05-01T07:00:00Z","updated_at":"2026-07-24T06:12:08Z","subjects":["Mathematics"],"languages":["English (en)"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/j0k7-mt40"],"render_values":[{"text":"https://doi.org/10.7936/j0k7-mt40","href":"https://doi.org/10.7936/j0k7-mt40","code":true}]}]},"links":{"outbound_url":"https://openscholarship.wustl.edu/etd_restrict/79","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Machtinger, Lawrence Arnold"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/etd_restrict/79"]},{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/j0k7-mt40"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The main objective of this paper is the study of rings with a relation which has all the properties of an order relation on a ring except, perhaps, for one: transitivity. Consequently, many of the results presented here are generalizations of well-known facts about transitively ordered rings; and most, but not all, of the conclusions of this paper are applicable to such rings.
"]},{"key":"dc:title","label":"Title","values":["Rings with a Not Necessarily Transitive Order Relation"]}]}],"canonical_facts":{"dc:creator":["Machtinger, Lawrence Arnold"],"dc:description.abstract":["The main objective of this paper is the study of rings with a relation which has all the properties of an order relation on a ring except, perhaps, for one: transitivity. Consequently, many of the results presented here are generalizations of well-known facts about transitively ordered rings; and most, but not all, of the conclusions of this paper are applicable to such rings.
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