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.

Modules (also known as profunctors or distributors) and morphisms among them subsume categories and functors and provide more general and abstract framework to explore the theory of structures. In this book we generalize and redevelop the basic notions and results of category theory using this framework of modules. Topics Chapter 1 introduces modules and cells among them. A moduleM ∶ X⇢A from a...

For a commutative algebra A over C, denote g=Der(A). module the smash product A#U(g) is called jet g-module, where U(g) universal enveloping of g. In present paper, we study modules in case A=C[t1±1,t2]. We show that A#U(g)≅D⊗U(L), D Weyl C[t1±1,t2,∂∂t1,∂∂t2], and L Lie subalgebra corresponding to Using isomorphism θ:L→m1,0Δ, m1,0Δ vector fields vanishing at point (1, 0), any irreducible finite...

There is growing evidence that Hilbert C*-module theory and the theory of wavelets and Gabor (i.e. Weyl-Heisenberg) frames are tightly related to each other in many aspects. Both the research fields can benefit from achievements of the other field. The goal of the talk given at the mini-workshop was to give an introduction to the theory of module frames and to Hilbert C*modules showing key anal...

Let £ be a split semisimple Lie algebra over a field of characteristic zero and <£ = 3C+ ]C«eA«£a be the rootspace decomposition of <£ relative to a splitting Cartan subalgebra 5C, where the subset A of 3C* is the corresponding root-system. Fix a simple system of roots {c*i, «2, • • • , ai}, for which the positive (resp. negative) roots are denoted by A+ (resp. A_). For a EA let Ra be the W...

Many known results on finite von Neumann algebras are generalized, by purely algebraic proofs, to a certain class C of finite Baer *-rings. The results in this paper can also be viewed as a study of the properties of Baer *-rings in the class C. First, we show that a finitely generated module over a ring from the class C splits as a direct sum of a finitely generated projective module and a cer...

In this paper, we characterize rank one preserving module maps on a Hilbert C∗−module and study its applications on free probability theory.

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

A Hilbert C∗-module is a generalisation of a Hilbert space for which the inner product takes its values in a C∗-algebra instead of the complex numbers. We use the bracket product to construct some Hilbert C∗-modules over a group C∗-algebra which is generated by the group of translations associated with a wavelet. We shall investigate bracket products and their Fourier transform in the space of ...

Improved baseplate materials are required to provide superior reliability and heat transfer as IGBT power density increases. The key is for the baseplate thermal coefficient of expansion (TCE) to be matched to the module design and to have sufficient thermal conductivity (κ). Aluminum Silicon Carbide (AlSiC), a metal matrix composite material, provides a TCE that is compatible with the attachme...