English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we mainly study the homological properties of dual modules over$k$-Gorenstein rings. For a right quasi $k$-Gorenstein ring $\Lambda$, we showthat the right self-injective dimension of $\Lambda$ is at most $k$ if and onlyif each $M \in$mod $\Lambda$ satisfying the condition that Ext$_{\Lambda}^i(M,\Lambda)=0$ for any $1\leq i \leq k$ is reflexive. For an $\infty$-Gorensteinring, we show that the big and small finitistic dimensions and theself-injective dimension of $\Lambda$ are identical. In addition, we show thatif $\Lambda$ is a left quasi $\infty$-Gorenstein ring and $M\in$mod $\Lambda$with grade$M$ finite, then Ext$_{\Lambda}^i($Ext$_{\Lambda^{op}}^i($Ext$_{\Lambda}^{{\rm grade}M}(M, \Lambda), \Lambda), \Lambda)=0$ ifand only if $i\neq$grade$M$. For a 2-Gorenstein ring $\Lambda$, we show that anon-zero proper left ideal $I$ of $\Lambda$ is reflexive if and only if$\Lambda /I$ has no non-zero pseudo-null submodule.

Homological Behavior of Auslander’s k-Gorenstein Rings