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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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##### References:
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