The regular algebra of a poset
The regular algebra of a poset
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偏序集的正则代数
DOI：
10.1090/s0002-9947-09-04884-3
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发表时间：
2008
影响因子：
1.3
通讯作者：
P. Ara
中科院分区：
文献类型：
--
作者：
P. Ara
设\(K\)为一个固定的域。我们以一种函子的方式给每个有限偏序集\(P\)附上一个冯·诺依曼正则\(K\)-代数\(Q_K(P)\)。我们证明了有限生成投射\(Q_K(P)\)-模的同构类的幺半群是由\(P\)生成的阿贝尔幺半群，且仅有的关系是当\(q<p\)在\(P\)中时\(p = p + q - q\)。这扩展了对于冯·诺依曼正则环的实现问题有正解的幺半群的类别。
Let K be a fixed field. We attach to each finite poset P a von Neumann regular K-algebra Q K (P) in a functorial way. We show that the monoid of isomorphism classes of finitely generated projective Q K (P)-modules is the abelian monoid generated by P with the only relations given by p = p+q q whenever q < p in P. This extends the class of monoids for which there is a positive solution to the realization problem for von Neumann regular rings.