On Noether $SPSD$-rings with a point-to-point quiver

V. V. Kirichenko, K. V. Usenko

National Taras Shevchenko University of Kyiv

Abstract: In the paper the term $SPSD$-ring for a semiabsolute and semidistributive ring is used. Let $R$ be the Jackobson radical of Noether reduced $SPSD$-ring $A$. We assume that the set $F(A)$ is nonempty. Then the quiver $Q(A)$ of $A$ is strongly connected. We show that the converse does not hold for Noether $SPSD$-rings.

UDC: 512.542

Received: 03.01.2008