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The lattice of \(\mathcal J\)-classes of \(({\mathcal J},\sigma)\)-irreducible monoids. II. (English) Zbl 0940.20066
An algebraic monoid \(M\) is called reductive if its unit group \(G\) is a reductive group. The paper is concerned with \(({\mathcal J},\sigma)\)-irreducible monoids, introduced by the author and L. E. Renner [in part I, J. Algebra 190, No. 1, 172-194 (1997; Zbl 0879.20035)]. This is a class properly containing \(\mathcal J\)-irreducible monoids. For the latter class, a general structure theorem for the lattice of \(\mathcal J\)-classes was obtained by M. S. Putcha and L. E. Renner [in J. Algebra 116, No. 2, 385-399 (1988; Zbl 0678.20039)]. In the paper review, the lattice of \(\mathcal J\)-classes of \(M\) is described if \(M\) is \(({\mathcal J},\sigma)\)-irreducible and the group \(G\) is of type \(D^2_n\) or \(A_n\), \(n\leq 3\).

MSC:
20M20 Semigroups of transformations, relations, partitions, etc.
20G15 Linear algebraic groups over arbitrary fields
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