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On flat covers in varieties

David Kruml (2008)

Commentationes Mathematicae Universitatis Carolinae

Flat covers do not exist in all varieties. We give a necessary condition for the existence of flat covers and some examples of varieties where not all algebras have flat covers.

On rings close to regular and p -injectivity

Roger Yue Chi Ming (2006)

Commentationes Mathematicae Universitatis Carolinae

The following results are proved for a ring A : (1) If A is a fully right idempotent ring having a classical left quotient ring Q which is right quasi-duo, then Q is a strongly regular ring; (2) A has a classical left quotient ring Q which is a finite direct sum of division rings iff A is a left TC -ring having a reduced maximal right ideal and satisfying the maximum condition on left annihilators; (3) Let A have the following properties: (a) each maximal left ideal of A is either a two-sided ideal...

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