This thesis is an investigation into the determination of the numbers of non-isomorphic rings that exist for some finite orders. Evidently very few writers have pursued this topic. D. M. Bloom, in answer to an earlier posed problem, gave the results for order four in the American Mathematical Monthly , volume 71, October, 1964. Beginning with an initial characterization, results are established giving the number of non-isomorphic rings which are additively cyclic for any finite order. For any prime order and any finite order whose only abelian group is cyclic, this then would give the total number of nonisomorphic rings of that order. Cayley tables are presented for orders six and ten, and Bloom's results are amplified and Cayley tables are presented for order four in chapter 3. Incomplete results for orders eight and nine, together with their Cayley tables are presented in chapters 4 and 5. Directions for further study are discussed in chapter 6.
","abstract_html":"<p>This thesis is an investigation into the determination of the numbers of non-isomorphic rings that exist for some finite orders. Evidently very few writers have pursued this topic. D. M. Bloom, in answer to an earlier posed problem, gave the results for order four in the American Mathematical Monthly , volume 71, October, 1964. Beginning with an initial characterization, results are established giving the number of non-isomorphic rings which are additively cyclic for any finite order. For any prime order and any finite order whose only abelian group is cyclic, this then would give the total number of nonisomorphic rings of that order. Cayley tables are presented for orders six and ten, and Bloom's results are amplified and Cayley tables are presented for order four in chapter 3. Incomplete results for orders eight and nine, together with their Cayley tables are presented in chapters 4 and 5. Directions for further study are discussed in chapter 6.</p>","abstract_has_math":false,"creators":["France, Robert Eugene"],"institution":null,"degree_name":"Master of Science (MS) in Mathematics","degree_level":"Thesis: EWU Only","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1973,"date_issued":"1973-01-01T08:00:00Z","date_published":"1973-01-01T08:00:00Z","updated_at":"2026-07-24T02:13:07Z","subjects":["Algebra"],"languages":[],"rights":["Access perpetually restricted to EWU users with an active EWU NetID"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.ewu.edu/theses/915","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["France, Robert Eugene"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis: EWU Only"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS) in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebra"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Access perpetually restricted to EWU users with an active EWU NetID"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.ewu.edu/theses/915"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis is an investigation into the determination of the numbers of non-isomorphic rings that exist for some finite orders. Evidently very few writers have pursued this topic. D. M. Bloom, in answer to an earlier posed problem, gave the results for order four in the American Mathematical Monthly , volume 71, October, 1964. Beginning with an initial characterization, results are established giving the number of non-isomorphic rings which are additively cyclic for any finite order. For any prime order and any finite order whose only abelian group is cyclic, this then would give the total number of nonisomorphic rings of that order. Cayley tables are presented for orders six and ten, and Bloom's results are amplified and Cayley tables are presented for order four in chapter 3. Incomplete results for orders eight and nine, together with their Cayley tables are presented in chapters 4 and 5. Directions for further study are discussed in chapter 6.
"]},{"key":"dc:title","label":"Title","values":["A study of some rings of finite power"]}]}],"canonical_facts":{"dc:creator":["France, Robert Eugene"],"dc:description.abstract":["This thesis is an investigation into the determination of the numbers of non-isomorphic rings that exist for some finite orders. Evidently very few writers have pursued this topic. D. M. Bloom, in answer to an earlier posed problem, gave the results for order four in the American Mathematical Monthly , volume 71, October, 1964. Beginning with an initial characterization, results are established giving the number of non-isomorphic rings which are additively cyclic for any finite order. For any prime order and any finite order whose only abelian group is cyclic, this then would give the total number of nonisomorphic rings of that order. Cayley tables are presented for orders six and ten, and Bloom's results are amplified and Cayley tables are presented for order four in chapter 3. Incomplete results for orders eight and nine, together with their Cayley tables are presented in chapters 4 and 5. Directions for further study are discussed in chapter 6.
"],"dc:identifier":["https://dc.ewu.edu/theses/915"],"dc:rights":["Access perpetually restricted to EWU users with an active EWU NetID"],"dc:subject":["Algebra"],"dc:title":["A study of some rings of finite power"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis: EWU Only"],"thesis:degree_name":["Master of Science (MS) in Mathematics"]},"updated_at":"2026-07-24T02:13:07Z"}