The soil nematode, Caenorhabditis elegans, occupies a central place in the short history of microRNA (miRNA) research. The converse is also true: miRNAs have emerged as key regulatory components in the life cycle of the worm, as well as numerous other organisms. Since the landmark discovery in 1993 of the first miRNA gene, lin-4, several other miRNAs have been characterized in detail in C. eleg...

In this article we investigate homological aspects of a skew complete intersection R, i.e. polynomial ring modulo an ideal generated by sequence regular normal elements. We compute the derived braided Hochschild cohomology R relative to and show its action on ExtR(M,N) is noetherian for finitely R-modules M N respecting braiding R. When parameters defining are roots unity use define support the...

We define and study the Milnor K-ring of a field F modulo a subgroup of the multiplicative group of F . We compute it in several arithmetical situations, and study the reflection of orderings and valuations in this ring. Introduction Let F be a field and let F× be its multiplicative group. The Milnor K-ring K ∗ (F ) of F is the tensor (graded) algebra of the Z-module F× modulo the homogenous id...

Let Lω(G) be a Beurling algebra on a locally compact abelian group G. We look for general conditions on the weight which allows the vanishing of continuous derivations of Lω(G). This leads us to introducing vector-valued Beurling algebras and considering the translation of operators on them. This is then used to connect the augmentation ideal to the behavior of derivation space. We apply these ...

Let $f: Arightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the property of coherence to the amalgamation $Abowtie^{f}J$. We provide necessary and sufficient conditions for $Abowtie^{f}J$ to be a coherent ring.