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Research Interests
Matrices
The theory of matrices plays an important role both within mathematics and in its applications. Within the theory of rings a natural question is how a
given ring is related to matrix rings or to variants of matrix rings. More specifically, it was noted in the literature that rings could be matrix rings despite
appearances to the contrary. This phenomenon has in part been explained by a criterion obtained here at Leeds. And further, more general, work is
currently in progress.
Ring Extensions
It is a common phenomenon (for example in several of the areas noted above) that rings occur as subrings, or extension rings, of better understood
rings. Many facets of the detailed relationship between such pairs of rings have been elucidated, and work on this is continuing.
Hereditary Noetherian Rings
The well-known theory of modules over a commutative Dedekind domain has now
largely been extended to the case of noncommutative hereditary Noetherian
prime rings (in joint work with Prof L.S.Levy
of Wisconsin); but some questions remain.
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