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Extending pioneering work by Weinberg, Conrad, McCleary, and others, we provide a systematic way of relating spaces of right orders on a partially ordered group, on the one hand, and spectral spaces of free lattice-ordered groups, on the other. The aim of the theory is to pave the way for further fruitful interactions between the study of right orders on groups and that of lattice-groups. Special attention is paid to the important case of orders on groups. [ABSTRACT FROM AUTHOR]

This article challenges Nicholas Wolterstorff’s rights-based reading of Old Testament orphans by arguing that the prophetic demand for their cause not only assumes a right-order ethos championed in the Torah, but in doing so exposes the shortcomings in how justice is defined for orphaned children within current rights ideology, whether theistic or not. I present the orphan’s historical trajectory towards becoming socially vulnerable as the final stage in the transition from the kinship-redeemer justice of Israelite village clans to the chesed justice of the patronage economy in emerging urban conditions. In light of these conditions, I show how the orphan laws in Deuteronomy are, counter to Wolterstorff’s claims of corruption, attempting to re-create in legal terms the kinship bond and chesed benevolence that defines the orphan’s justice as the return to a family. I argue that the prophet does not blame inherently corrupt laws, but rather blames patrons and elders who have ignored good laws and ignored right-order by forgetting their brothers’ and sons’ children. [ABSTRACT FROM AUTHOR]

Let $A$ be a ring, and let $T(A)$ and $N(A)$ be the set of all the regular elements of $A$ and the set of all nonregular elements of $A$, respectively. It is proved that $A$ is a right order in a right uniserial ring if and only if the set of all regular elements of $A$ is a left ideal in the multiplicative semigroup $A$ and for any two elements $a\_1$ and $a\_2$ of $A$, either there exist two elements $b\_1\backslash in\; A$ and $t\_1\backslash in\; T(A)$ with $a\_1b\_1=a\_2t\_1$ or there exist two elements $b\_2\backslash in\; A$ and $t\_2\backslash in\; T(A)$ with $a\_2b\_2=a\_1t\_2$. A right distributive ring $A$ is a right order in a right uniserial ring if and only if the set $N(A)$ is a left ideal of $A$. If $A$ is a right distributive ring such that all its right divisors of zero are contained in the Jacobson radical $J(A)$ of $A$, then $A$ is a right order in a right uniserial ring. [ABSTRACT FROM AUTHOR]