Islam, being a comprehensive religion, provides numerous, obligatory and voluntary distributive measures and strategies such as Zakat, Zakat-al-fitr, inheritance, obligatory maintenance to poor relatives, Manihe, etc., in order to prevent the concentration of wealth in few hands and to guarantee the fulfillment of basic needs and minimum level of life for all of citizens. The paper discusses these measures thoroughly and examines the efficiency of Islamic system of distribution and redistribution of income, wealth and other resources in eliminating poverty and reducing the gaps between the rich and the poor.

The concepts of regular filters and π--filters are introduced in distributive lattices. A set of equivalent conditions is given for a D-filter to become a regular filter. For every D-filter, it is proved that there exists a homomorphism whose dense kernel is a regular filter. π--filters are characterized in terms of regular filters and congruences. Some equivalent conditions are given for the space of all prime π-filters to become a Hausdorff space.

The concept of K-filters is introduced in distributive lattices and studied some properties of these classes of filters. Some necessary and sufficient conditions are derived for every π-filter of a distributive lattice to become a K-filter. Some equivalent conditions are derived for every D-filter of a distributive lattice to become a K-filter. Quasi-complemented lattices are characterized with the help of K-filters.

Let R  be a Z-graded commutative ring with identity. Several characterizations of graded distributive modules will be investigate.

The notion of ω,-filters is introduced in distributive lattices and their properties are studied. A set of equivalent conditions is derived for every maximal filter of a distributive lattice to become an ω,-filter which leads to a characterization of quasi-complemented lattices. Some sufficient conditions are derived for proper D-filters of a distributive lattice to become an ω,-filter. Finally, ω,-filters of a distributive lattice are characterized with the help of minimal prime D-filters.

Contract law is one substantial pillar of Distribution. Contract parties understand themselves to be engaged in a strictly bilateral exchange to which the parties jointly and exclusively control the terms. Upon breach of the Contract, the suit is based upon a conception of commutative Justice. Distributive justice is concerned with the fair allocation of resources among community members. Liberals who oppose the use of contract law as a redistributive device believe that distributional objectives are always better achieved through the tax system than through the detailed regulation of individual transactions. Contracts involve just two people and distributive justice involves many. The claims of distributive justice might require that we enlist contract as a tools to pursue more equitable distributions. A related claim would be that we should interpret interpersonal entitlements in such a way that they do not exacerbate distributive Injustice. Another focus is on the effects of contract on distribution rather than the effect of distribution on the independent morality of contract. Contingent accounts treat on social context and background involuntary duties. The value of promise and the efficacy of contract depend on the kind of relation from which it arises and their social starting points. There is no categorical reason for barring distributive considerations from the contract regulation. Most of the rules that make up contract law are defaults; which could be choose according to distributional considerations, the list that illustrate the distributive nature of contract rules is countless, and spills over into mutual assent, interpretation, breach…

In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left k-radicals  (a) = fx 2 S j a l 􀀀 ! 1 xg induced by the transitive closure l 􀀀 ! 1 of the relation l 􀀀 ! which induce the equivalence relation  . Again non-transitivity of l 􀀀 ! yields an expanding family f l 􀀀 ! ng of binary relations which associate subsets  n(a) for all a 2 S, which again induces an equivalence relation  n. We also de ne  ( n)-simple semirings, and characterize the semirings which are distributive lattices of  ( n)-simple semirings.

In this article, we present the concept of an N −ideal within the structure of an Almost Distributive Lattice (ADL). We demonstrate that the collection of N −ideals constitutes a distributive lattice, which is distinct from and not a sublattice of the lattice of ideals in an ADL. Additionally, we define N −lets in ADLs. We derive the necessary and sufficient conditions for an ideal to be classified as an N −ideal using N −lets. Finally, we establish the conditions required for an ADL to achieve the property of being soft relatively complemented.

The notion of w−filters is introduced in an Almost Distributive Lattice(ADL) and properties are investigated. A necessary and sufficient condition is derived for a maximal filter of an ADL to become a w−filter which leads to a characterization of a quasi-complemented ADL. Also, w−filters of an ADL are characterized in terms of minimal prime D−filters.