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On the construction and the realization of wild monoids

Pavel Růžička (2018)

Archivum Mathematicum

We develop elementary methods of computing the monoid 𝒱 ( R ) for a directly-finite regular ring R . We construct a class of directly finite non-cancellative refinement monoids and realize them by regular algebras over an arbitrary field.

P -clean rings.

Chen, Weixing (2006)

International Journal of Mathematics and Mathematical Sciences

P ( r , m ) near-rings.

Balakrishnan, R., Suryanarayanan, S. (2000)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Products of small modules

Peter Kálnai, Jan Žemlička (2014)

Commentationes Mathematicae Universitatis Carolinae

Module is said to be small if it is not a union of strictly increasing infinite countable chain of submodules. We show that the class of all small modules over self-injective purely infinite ring is closed under direct products whenever there exists no strongly inaccessible cardinal.

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