| Abstract |
Hibi rings and their de ning ideals are attached in a natural way to nite distributive lattices. They were fi rst introduced by Hibi in 1987. In the last decades, many authors have investigated various properties and invariants of Hibi rings. In this presentation, we will discuss certain characteristics of Hibi rings and Grobner Basis of the Hibi ideal. Moreover, we will discuss rank bounded Hibi subrings. Moreover, we will discuss rank bounded Hibi subrings. They were introduced by Aramova, Herzog and Hibi in 2000.
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