$\mu$−filters of Almost Distributive Lattices

CJM Vol. 10 (December 2018), pp. 53 – 65.


The concept of $\mu$−filters is introduced in an Almost Distributive Lattice(ADL) and studied their properties in terms of dual annihilator filters of an ADL. Observed that the set of all dual annihilator filters of an ADL forms a complete Boolean algebra. Derived equivalent conditions for every filter of an ADL becomes a dual annihilator filter by assuming the property that every proper filter is non co-dense. Also, observed that $\mu$ is homomorphism of $F(L)$ in to $I(\mathfrak{A}^+(L))$. Characterized $\mu$−filter in element wise and verified that every minimal prime filter of an ADL is a $\mu$−filter. Finally, we proved that the intersection of all prime $\mu$−filters is the set of all maximal elements of an ADL.

2000 Mathematics Subject Classification: 

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