We construct irreducible modules Vα, α ∈ C over W3 algebra with c = −2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W3 algebra with c = −2. Highest weights of modules Vα, α ∈ C with respect to the full (two-dimensional) Cartan subalgebra of W3 algebra are ( 1 2α(α − 1), 16α(α − 1)(2α − 1) ) . They are parametrized by points (t, w) on a rat...

In this paper, we introduce a family of indecomposable finitedimensional graded modules for the twisted current algebras. These modules are indexed by an |R+|-tuple of partitions ξ = (ξ)α∈R+ satisfying a natural compatibility condition. We give three equivalent presentations of these modules and show that for a particular choice of ξ these modules become isomorphic to Demazure modules in variou...

If H is a Hopf algebra with bijective antipode and α, β ∈ AutHopf (H), we introduce a category HYD (α, β), generalizing both Yetter-Drinfeld modules and anti-Yetter-Drinfeld modules. We construct a braided T-category YD(H) having all the categories HYD (α, β) as components, which ifH is finite dimensional coincides with the representations of a certain quasitriangular T-coalgebra DT (H) that we...

let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.

The categorical treatment of fuzzy modules presents some problems, due to the well known fact that category is not abelian, and even normal. Our aim give a representation inside generalized modules, in fact, functor category, Mod−P, which Grothendieck category. To do that, first we consider preadditive P, defined by interval P=(0,1], build torsionfree class J hereditary torsion theory finally i...

let $r$ be a commutative noetherian ring with non-zero identity, $fa$ an ideal of $r$, and $x$ an $r$--module. here, for fixed integers $s, t$ and a finite $fa$--torsion $r$--module $n$, we first study the membership of $ext^{s+t}_{r}(n, x)$ and $ext^{s}_{r}(n, h^{t}_{fa}(x))$ in the serre subcategories of the category of $r$--modules. then, we present some conditions which ensure the exi...

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

PURPOSE To develop an efficient 31 P magnetic resonance spectroscopy (MRS) method for measuring creatine kinase (CK) activity, adenosine triphosphate (ATP) synthesis, and motion dynamics in the human brain at 7 Tesla (T). METHODS Three band inversion modules differing in center frequency were used to induce magnetization transfer (MT) effect in three exchange pathways: (i) CK-mediated reactio...