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On rings with finite number of orbits

Małgorzata Hryniewicka and Jan Krempa

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Let $R$ be an associative unital ring with the unit group $U(R)$. Let $\mathcal{S}$ denote one of the following sets: the set of elements of $R$, of left ideals of $R$, of principal left ideals of $R$, or of ideals of $R$. Then the group $U(R)\times U(R)$ acts on the set $\mathcal{S}$ by left and right multiplication. In this note we are going to discuss some properties of rings $R$ with a finite number of orbits under the action of $U(R)\times U(R)$ on $\mathcal{S}$.

Article information

Publ. Mat., Volume 58, Number 1 (2014), 233-249.

First available in Project Euclid: 20 December 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16P99: None of the above, but in this section 16U60: Units, groups of units 16L30: Noncommutative local and semilocal rings, perfect rings

Groups of units $U(R)$-orbits semilocal rings semiprimary rings


Hryniewicka, Małgorzata; Krempa, Jan. On rings with finite number of orbits. Publ. Mat. 58 (2014), no. 1, 233--249.

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