Two-Sided Essential Submodules of Q(R)

• Autores: Albrecht Ulrich
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 1, 2007, págs. 103-123
• Idioma: inglés
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• Resumen

  • The focus of this paper are essential submodules A of the maximal right ring of quotients, Q(R), of a right non-singular ring R. Since Q(R) is a R-R-bimodule, particular attention is given to submodules of the right R-module Q(R) which are also submodules of the left R-module Q(R). In this discussion, properties of R which are inherited by intermediate rings S contained between R and Q(R) are investigated. The results obtained are used to discuss homological properties of essential submodules A of Q(R). In particular, the paper addresses the question when S-closed submodules of finite direct sums of copies of A are direct summands.