Let E be a cyclic extension of pth-power degree of a field F of characteristic p. For all m, s ∈ N, we determine KmE/p sKmE as a (Z/pZ)[Gal(E/F )]-module. We also provide examples of extensions for which all of the possible nonzero summands in the decomposition are indeed nonzero. Let F be a field of characteristic p. Let KmF denote the mth Milnor K-group of F and kmF = KmF/pKmF . (See, for ins...

a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.

The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras [R, FFT]. We prove that generically their action on finitedimensional modules is diagonalizable and their joint spectra are in bijection with the set of monodromy-free G -opers on P with regular singularity at one point and irregular singula...

In this paper, by using Gröbner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded...

Let R be a ring. A right R-module is said to C-flat if the kernel of any epimorphism B → C-pure in B, i.e. induced map Hom(C,B) Hom(C,A) surjective for cyclic C. Projective modules are and weakly-flat neat-flat. In this article, it discussed connections between C-flat, weakly-flat, neat-flat singly flat modules. It shown that coincide with singly-projective over arbitrary rings. Next, several c...

The group Am of automophisms of a one-rooted m-ary tree admits a diagonal monomorphism which we denote by x. Let A be an abelian state-closed (or self-similar) subgroup of Am. We prove that the recurrence and tree-topological closure A∗ of A is additively a finitely presented Zm [[x]]module where Zm is the ring of m-adic integers. Moreover, if A∗ is torsion-free then it is a finitely generated ...

Syringomycin, a lipopeptidolactone assembled from nine amino acid monomers by four enzymes, SyrB1, SyrB2, SyrC, and SyrE, is a cyclic nonribosomal peptide made by plant-associated Pseudomonas spp. This assembly is unusual because the terminal residue, 4-chlorothreonine, has been proposed to be added in trans since the ninth module of the megasynthetase SyrE lacks an adenylation domain required ...

The cyclic homology H C*(A) of an associative algebra with unit A over a field k of characteristic zero was introduced by A. Connes [C1], and extended to arbitrary commutative rings k in [LQ]. It comes equipped with a natural degree (-2) k-linear map S: HC*(A)~HC*_2(A). We will occasionally write S as SA to indicate dependence on the ring A; the map SA provides HC*(A) with a natural k[u] co-mod...

We present a general distributed control algorithm for achieving locomotion of a self-reconfigurable robot. In this algorithm each module continuously performs a cyclic sequence of actions with a period . When a specified fraction of this period has elapsed a signal is sent to all child modules. Upon receiving this signal the child module resets its action sequence making it delayed compared to...

It is shown that every commutative local ring of bounded module type is an almost maximal valuation ring. We say that an associative commutative unitary ring R is of bounded module type if there exists a positive integer n such that every finitely generated R-module is a direct sum of submodules generated by at most n elements. For instance, every Dedekind domain has bounded module type with bo...