dc.contributor.advisor v d Walt, AP J dc.contributor.author Fransman, Andrew dc.date.accessioned 2023-06-13T13:21:18Z dc.date.available 2023-06-13T13:21:18Z dc.date.issued 1984 dc.identifier.uri http://hdl.handle.net/11394/10223 dc.description >Magister Scientiae - MSc en_US dc.description.abstract In this chapter we supply all the necessary definitions as well as the required results needed in this work. All the notation and terminology will also be explained carefully. §1 DEFINITIONS AND NOTATION R will always denote a ring with identity and Mn(R) will denote the ring of nxn matrices over R. As usual the ring of integers, the ring of integers modulo n and the field of rational numbers will be denoted by z, Zn and Q respectively. ng of polynomials in the indeterminate x. The constant term of any polynomial fER[x] will be denoted by const(f). Ideal (or module) will always mean left ideal (or module). In order to simplify notation we shall adopt the convention M,N, M/N, etc. in stead of RM' RN, RM/N, etc., for left Rmodules. It will however always be evident from the context, to which ring R we are referring. Max(R) will denote the collection of all maximal left ideals of R. Mand N will be generic symbols for maximal left ideals. Normally mappings will be written on the left except in the cases of Proposition 1.12 and 1.15. R will be considered as a subring of Mn(R) via the natural embedding r + diag(r, ••• ,r). en_US dc.language.iso en en_US dc.publisher University of the Western Cape en_US dc.subject Terminology en_US dc.subject Covariant en_US dc.subject Morita equivalent en_US dc.subject Maximal submodule en_US dc.title Maximal left ideals and idealizers in matrix rings en_US dc.rights.holder University of the Western Cape en_US
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