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Properties of G-atoms and full Galois covering reduction to stabilizers

Piotr Dowbor (2000)

Colloquium Mathematicae

Given a group G of k-linear automorphisms of a locally bounded k-category R it is proved that the endomorphism algebra E n d R ( B ) of a G-atom B is a local semiprimary ring (Theorem 2.9); consequently, the injective E n d R ( B ) -module ( E n d R ( B ) ) * is indecomposable (Corollary 3.1) and the socle of the tensor product functor - ⊗ R B * is simple (Theorem 4.4). The problem when the Galois covering reduction to stabilizers with respect to a set U of periodic G-atoms (defined by the functors Φ U : ∐ B ∈ U m o d k G B → m o d ( R / G ) and Ψ U : m o d ( R / G ) → ∏ B ∈ U m o d k G B )is full (resp. strictly full) is studied...

Prüfer rings with involution

Ismail M. Idris (2003)

Czechoslovak Mathematical Journal

The concept of a Prüfer ring is studied in the case of rings with involution such that it coincides with the corresponding notion in the case of commutative rings.

Pseudocomplements in sum-ordered partial semirings

Jānis Cīrulis (2007)

Discussiones Mathematicae - General Algebra and Applications

We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several...

Pseudoringe

Stanislav Židek (1972)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica-Physica-Chemica

Pseudospectra and matrix behaviour

Thomas Ransford (2010)

Banach Center Publications

We study the extent to which the pseudospectra of a matrix determine other aspects of its behaviour, such as the growth of its powers and its unitary equivalence class.

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