The genes encoding aspartate kinase (ask), homoserine dehydrogenase (hom), homoserine kinase (thrB) and threonine synthase (thrC) from the obligate methylotroph Methylobacillus flagellatus were cloned. In maxicells hom and thrC directed synthesis of 51 and 48 kDa polypeptides, respectively. The hom, thrB and thrC genes and adjacent DNA areas were sequenced. Of the threonine biosynthesis genes, ...

The main feature of Hom-algebras is that the identities defining structures are twisted by linear maps. purpose this paper to introduce and study a Hom-type generalization pre-Malcev algebras, called Hom-pre-Malcev algebras. We also notion Kupershmidt operators Hom-Malcev algebras show connections between using operators. generalize Hom-pre-Lie Hom-alternative setting fit into bigger framework ...

The purpose of this paper is to study Sabinin algebras Hom-type. It shown that Lie, Malcev, Bol and other Hom-type are naturally To end, we provide a general key construction establish relationship between identities some class Hom-algebras ordinary algebras. Moreover, discuss new concept Hom-bialgebra, in relation with universal enveloping Hom-algebras. A based on primitive elements provided.

Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...

This paper is devoted to the construction of Hom-Leibniz H-pseudoalgebras, which unify Hom-Lie Leibniz H-pseudoalgebras and algebras. Firstly, we give theorem obtain a class H-pseudoalgebras. We also construct Hom- from different perspectives, including (resp. Hom-Lie, Hom-associative) their representations, Homassociative) Thenwegive some properties representations Hom-LeibnizH-pseudoalgebras....

The aim of this work is to introduce and study the notions Hom-pre-Jordan algebra Hom-J-dendriform which generalize Hom-Jordan algebras. algebras are regarded as underlying algebraic structures behind Rota-Baxter operators O-operators introduced in paper. also analogues Hom-pre-Lie for anti-commutator a left multiplication operator gives representation algebra. On other hand, analogue Hom-dendr...

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel’d’s quasitriangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel’d’s quantum env...

In the category of Hom-Leibniz algebras we introduce the notion of Hom-corepresentation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, univer...

This paper studies homogeneously Suslin (hom) sets of reals in tame mice. The following results are established: In 0¶ the hom sets are precisely the ̃ 11 sets. In Mn every hom set is correctly ̃ 1n+1, and (δ + 1)-universally Baire where δ is the least Woodin. In Mω every hom set is <λ-hom, where λ is the supremum of the Woodins. §

Proof: For f ∈ Hom(X,A), i ◦ f = 0 implies (i ◦ f)(x) = 0 for all x ∈ X, and then f(x) = 0 for all x since i is injective. Thus, Hom(X,A)→ Hom(X,B) is injective, giving exactness at the left joint. Since q ◦ i = 0, any f ∈ Hom(X,A) is mapped to 0 ∈ Hom(X,C) by f → q ◦ i ◦ f . That is, the image of i ◦ − is contained in the kernel of q ◦ −. On the other hand, when g ∈ Hom(X,B) is mapped to q ◦ g...