Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1966 Meet representations in upper continuous modular lattices James Elton Delany Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Mathematics Commons Recommended Citation Delany, James Elton, "Meet representations in upper continuous modular lattices " (1966). Retrospective Theses and Dissertations. 2894. https://lib.dr.iastate.edu/rtd/2894 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact
[email protected]. This dissertation has been microiihned exactly as received 66-10,417 DE LA NY, James Elton, 1941— MEET REPRESENTATIONS IN UPPER CONTINU OUS MODULAR LATTICES. Iowa State University of Science and Technology Ph.D., 1966 Mathematics University Microfilms, Inc.. Ann Arbor, Michigan MEET REPRESENTATIONS IN UPPER CONTINUOUS MODULAR LATTICES by James Elton Delany A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of The Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Mathematics Approved: Signature was redacted for privacy. I _ , r Work Signature was redacted for privacy. Signature was redacted for privacy. Iowa State University of Science and Technology Ames, Iowa 1966 il TABLE OP CONTENTS Page 1. INTRODUCTION 1 2. TORSION ELEMENTS, TORSION FREE ELEMENTS, AND COVERING CONDITIONS 4 3. ATOMIC LATTICES AND UPPER CONTINUITY 8 4. COMPLETE JOIN HOMOMORPHISMS 16 5. TWO HOMOMORPHISMS 27 6.