Hao, Zhifeng Invariant basis number of the ring of Morita context. (English) Zbl 0888.16003 Chin. Sci. Bull. 42, No. 8, 633-636 (1997). A ring \(R\) is said to be an IBN ring if for every free left \(R\)-module \(F\) every two bases of \(F\) have the same cardinality. In this note conditions are shown when the ring of a Morita context \(T=\left(\begin{smallmatrix} R &M\\ N &S\end{smallmatrix}\right)\) is an IBN ring.Theorem. Let \(M\) (\(N\)) be a finitely generated right (left) \(S\)-module. The ring \(T\) is an IBN ring if and only if \(R\) is an IBN ring or \(S\) is an IBN ring. Some corollaries are formulated, in particular: \(M_n(R)\) is an IBN ring if and only if \(R\) is an IBN ring. Reviewer: A.I.Kashu (Kishinev) MSC: 16D90 Module categories in associative algebras 16D40 Free, projective, and flat modules and ideals in associative algebras 16S50 Endomorphism rings; matrix rings Keywords:endomorphism rings; free left modules; finitely generated right modules; rings of Morita contexts; IBN rings PDFBibTeX XMLCite \textit{Z. Hao}, Chin. Sci. Bull. 42, No. 8, 633--636 (1997; Zbl 0888.16003) Full Text: DOI References: [1] Cohn, P. M., Some remarks on the invariant basis property,Topology, 1966, 5: 215. · Zbl 0147.28802 [2] McConnell, J. C., Robson, J. C..Noncommutation Noetherian Rings. New York: Wiley-Interscience, 1987 · Zbl 0644.16008 [3] Hao Zhifeng. Tong Wenting, Global dimension of ring \(T = \left( {\begin{array}{*{20}c} R & M N & S \end{array}} \right)_{(\theta , \psi )} \) Sciencein China, Ser. A, 1995, 38: 1025. [4] Rotman, J. J.,An Introduction to Homological Algebra, New York: Academic Press, 1979. · Zbl 0441.18018 [5] Cohn, P. M.,Algebra, Vol. 2, New York: John Wiley and Sons, 1977. [6] Tong Wenting, Some results on IBN rings,J. of Nunjing Univ. Math. Biquarterly (in Chinese),1984, 1: 217. · Zbl 0564.16004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.