Let $\Lambda=\left(\begin{smallmatrix} A&M 0&B \end{smallmatrix}\right)$ be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective $\Lambda$-modules under the condition that $M$ is a cocompatible $(A,B)$-bimodule, we establish a recollement of the stable category $\overline{\rm Ginj(\Lambda)}$. We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over $\Lambda$., Chao Wang, Xiaoyan Yang., and Obsahuje bibliografii
Several characterizations of 0-distributive posets are obtained by using the prime ideals as well as the semiprime ideals. It is also proved that if every proper l-filter of a poset is contained in a proper semiprime filter, then it is 0-distributive. Further, the concept of a semiatom in 0-distributive posets is introduced and characterized in terms of dual atoms and also in terms of maximal annihilator. Moreover, semiatomic 0-distributive posets are defined and characterized. It is shown that a 0-distributive poset P is semiatomic if and only if the intersection of all non dense prime ideals of P equals (0]. Some counterexamples are also given.
The concept of a 0-ideal in 0-distributive posets is introduced. Several properties of 0-ideals in 0-distributive posets are established. Further, the interrelationships between 0-ideals and α-ideals in 0-distributive posets are investigated. Moreover, a characterization of prime ideals to be 0-ideals in 0-distributive posets is obtained in terms of non-dense ideals. It is shown that every 0-ideal of a 0-distributive meet semilattice is semiprime. Several counterexamples are discussed.