Nicholson, W. KeithBryden, John Milton2005-07-192005-07-191979Bryden, J. M. (1979). Weakly primitive rings (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/18215http://hdl.handle.net/1880/13762Bibliography: p. 84.Everyone who has aquainted himself with some ring theory is familiar with Jacobson's classical structure theorem for primitive rings. This thesis is based on the study of a class of prime rings which satisfy a weaker criterion than the class of primitive rings. The study of prime rings plays a significant role in modern ring theory, and since Jacobson's result includes the Wedderburn-Artin Theorem, which is the major structure theorem for rings possessing descending chain conditions, as a special case, the importance of Jacobson's result cannot be understated. The central concepts and results presented here were originally proved by Zelmanowitz in [9] and Amitsur in [1]. We call a module compressible provided that for any non- zero submodule N of M, HomR(MN) contains a monomorphism, and is called monoform when each non- zero element of HomR(N,M) is injective. Our major result (Zelmanowitz [9]) shows that a ring possessing a faithful compressible monoform module satisfies a weakened density criterion (such rings are called weakly primitive). Next we define a module R Mto be prime [ semiprime] if for any non- zero elements m,m 1 E M there exists f E HomR(M,R) such that (nif)m 1 0 0 [(mnf)m 0 0] and we specialize Zelmanowitz' result to the case of prime and semiprime modules with certain maximum conditions ( Zelmanowitz [ 8 ]). Finally, we give an exposition of some results by Nicholson, Watters and Zelmanowitz in [7] concerning derived rings of weakly primitive rings. Among other interesting results we prove that polynomial rings and certain group rings over weakly primitive rings are weakly primitive as well.vi, 84 leaves ; 30 cm.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.QA 247 B58 1979 FicheRings (Algebra)master thesis10.11575/PRISM/18215QA 247 B58 1979 Fiche