### Almost principal element lattices.

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In this paper we study primary elements in Prüfer lattices and characterize $\alpha $-lattices in terms of Prüfer lattices. Next we study weak ZPI-lattices and characterize almost principal element lattices and principal element lattices in terms of ZPI-lattices.

In this paper we establish some conditions for an almost $\pi $-domain to be a $\pi $-domain. Next $\pi $-lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for $\pi $-rings.

In this paper we investigate prime divisors, ${B}_{w}$-primes and $zs$-primes in $C$-lattices. Using them some new characterizations are given for compactly packed lattices. Next, we study Noetherian lattices and Laskerian lattices and characterize Laskerian lattices in terms of compactly packed lattices.

In this paper we establish some new characterizations for $Q$-rings and Noetherian $Q$-rings.

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