Characterization of Some Ring Properties in Incidence Algebras

Abstract

Let R be a ring with identity and I(X, R) be the incidence algebra of a locally finite partially ordered set X over R. In this article, we investigate the necessary and sufficient conditions for the incidence ring to be Ikeda-Nakayama, nil injective, NI, reduced, nonsingular and Kasch ring.

Key Words:

• Ikeda-Nakayama ring
• Incidence algebra
• Kasch ring
• Nil-injective ring
• Singular ideal

2000 Mathematics Subject Classification:

• 16S99
• 16W99
• 16N40

ACKNOWLEDGEMENT

We would like to thank Professor Cemal Koç, Professor İsmail Güloğlu, and Professor Eugene Spiegel for their valuable input in this work.

Dedicated to the memory of Professor Cemal Koç.

Notes

Communicated by M. Cohen.