The singular ideal and the socle of incidence rings
Let $R$ be a ring with identity and $I(X,R)$ be the incidence ring of a locally finite partially ordered set $X$ over $R.$ In this paper, we compute the socle and the singular ideal of the incidence ring for some $X$ in terms of the socle of $R$ and the singular ideal of $R$, respectively.
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- [1] F. Al-Thukair, S. Singh and I. Zaguia, Maximal ring of quotients of an incidence
algebra, Arch. Math. 80, 358–362, 2003.
- [2] S. Esin, M. Kanuni and A. Koç, Characterization of some ring properties in incidence
algebras, Comm. Algebra, 39 (10), 3836–3848, 2011.
- [3] M. Kanuni, Dense ideals and maximal quotient rings of incidence algebras, Comm.
Algebra, 31 (11), 5287–5304, 2003.
- [4] T.Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics 189, New
York-Berlin, Springer-Verlag, 1999.
- [5] E. Spiegel, Essential ideals of incidence algebras, J. Austral. Math. Soc. (Series A),
68, 252–260, 2000.
- [6] E. Spiegel and C.J. O’Donnell, Incidence Algebras, Monographs and Textbooks in
Pure Appl. Math. 206, New York, Marcel Dekker, 1997.