Displaying similar documents to “Complete residue systems in the ring of matrices of rational integers.”

An inverse matrix of an upper triangular matrix can be lower triangular

Waldemar Hołubowski (2002)

Discussiones Mathematicae - General Algebra and Applications

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In this note we explain why the group of n×n upper triangular matrices is defined usually over commutative ring while the full general linear group is defined over any associative ring.

Hopfian and co-Hopfian objects.

Kalathoor Varadarajan (1992)

Publicacions Matemàtiques

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The aim of the present paper is to study Hopfian and Co-Hopfian objects in categories like the category of rings, the module categories A-mod and mod-A for any ring A. Using Stone's representation theorem any Boolean ring can be regarded as the ring A of clopen subsets of compact Hausdorff totally disconnected space X. It turns out that the Boolean ring A will be Hopfian (resp. co-Hopfian) if and only if the space X is co-Hopfian (resp. Hopfian) in the category . For any compact Hausdorff...