Semirings with descending chain condition and without nilpotent elements
Semirings without zero divisors.
Semisimple Algebras and a Cancellation Law.
Semisimple completed group rings.
Semisimple ring spectra.
Semisimplicity and global dimension of a finite von Neumann algebra
We prove that a finite von Neumann algebra is semisimple if the algebra of affiliated operators of is semisimple. When is not semisimple, we give the upper and lower bounds for the global dimensions of and This last result requires the use of the Continuum Hypothesis.
Separable adel algebras and a presentation of Weil groups.
Separable Algebren über kommutativen Ringen.
Separable and Frobenius monoidal Hom-algebras
As generalizations of separable and Frobenius algebras, separable and Frobenius monoidal Hom-algebras are introduced. They are all related to the Hom-Frobenius-separability equation (HFS-equation). We characterize these two Hom-algebraic structures by the same central element and different normalizing conditions, and the structure of these two types of monoidal Hom-algebras is studied. The Nakayama automorphisms of Frobenius monoidal Hom-algebras are considered.
Separable functors for the category of Doi Hom-Hopf modules
Let be the category of Doi Hom-Hopf modules, be the category of A-Hom-modules, and F be the forgetful functor from to . The aim of this paper is to give a necessary and suffcient condition for F to be separable. This leads to a generalized notion of integral. Finally, applications of our results are given. In particular, we prove a Maschke type theorem for Doi Hom-Hopf modules.
Separable functors in corings.
Separable group-ring extensions.
Separable K-linear categories
We define and investigate separable K-linear categories. We show that such a category C is locally finite and that every left C-module is projective. We apply our main results to characterize separable linear categories that are spanned by groupoids or delta categories.
Separable Moduln von Algebren über Ringen.
Separable subalgebras of a class of Azumaya algebras.
Separative P.I. semigroups are embeddable into a semilattice of groups.
Séries formelles rationnelles et reconnaissables
Séries rationnelles à plusieurs variables non commutatives, Hadamard-inversibles
Serre functors for Lie algebras and superalgebras
We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category associated to a semi-simple complex finite dimensional Lie algebra. We further show that our realization carries over to classical Lie superalgebras in many cases. Along the way we prove that category and its parabolic generalizations for classical Lie superalgebras are categories with full projective functors. As an application we prove that in many cases the endomorphism algebra of the basic...
Serre Theorem for involutory Hopf algebras
We call a monoidal category C a Serre category if for any C, D ∈ C such that C ⊗ D is semisimple, C and D are semisimple objects in C. Let H be an involutory Hopf algebra, M, N two H-(co)modules such that M ⊗ N is (co)semisimple as a H-(co)module. If N (resp. M) is a finitely generated projective k-module with invertible Hattory-Stallings rank in k then M (resp. N) is (co)semisimple as a H-(co)module. In particular, the full subcategory of all finite dimensional modules, comodules or Yetter-Drinfel’d...