In this paper, we solve two problems concerning the ideally conjunctive join-semilattices. First, we show that \(L/R^1({{\,\textrm{Id}\,}}L)|_L\) is ideally conjunctive for all join-semilattices L. Then we characterize those ideally conjunctive join-semilattices L such that \({{\,\textrm{coz}\,}}a\) is compact for all \(a\in L.\) Moreover, we give the definition of conjunctive posets and prove that the category of ideally conjunctive join-semilattices and join homomorphisms is reflective in the category of conjunctive posets and weakly ideal-continuous maps. As a corollary, we obtain the free ideally conjunctive join-semilattices over conjunctive posets.

在本文中，我们解决了有关理想合取连接半格的两个问题。首先，我们证明\(L/R^1({{\,\textrm{Id}\,}}L)|_L\)对于所有连接半格子L来说是理想的合取。然后我们描述那些理想的合取连接半格L，使得\({{\,\textrm{coz}\,}}a\)对于所有\(a\in L.\)都是紧凑的。此外，我们给出了合取偏序集，并证明理想合取连接半格和连接同态的范畴反映在合取偏序集和弱理想连续映射的范畴中。作为推论，我们获得了合取偏序集上的自由理想合取连接半格。