$(m,n)$-Quasitilted and $(m,n)$-almost hereditary algebras

Almost Regular Auslander-reiten Components and Quasitilted Algebras

The problem of giving a general description of the shapes of AuslanderReiten components of an artin algebra has been settled for semiregular components (see [4, 9, 14]). Recently, S. Li has considered this problem for components in which every possible path from an injective module to a projective module is sectional. The result says that such a component is embeddable in some ZZ∆ with ∆ a quiv...

Mixed valency in polynuclear Mn/Mn, Mn/Mn and Mn/Mn/Mn clusters: a foundation for high-spin molecules and single-molecule magnets

Mixed-valent Mn/O dinuclear and polynuclear molecular compounds containing Mn are almost without exception trapped valence. Large differences between the strengths of the exchange interactions within MnMn, MnMn and MnMn pairs lead to situations where MnMn interactions, the strongest of the three mentioned and antiferromagnetic in nature, dominate the intramolecular spin alignments in trinuclear...

The Algebras Mn , n ( E ) and Mn ( E ) ⊗ E in Positive Characteristic

In characteristic zero the algebras Mn(E)⊗E andMn,n(E) appear in the list of non-trivial verbally-prime algebras. Verbally-prime algebras play a proeminent role in Kemer’s results about structure of the varieties of associative algebras in characteristic zero (see [8] for a detailed account of it). Recently, some new results have been obtained about the behavior of polynomial identities satisfi...

Tilting Theory and Quasitilted Algebras

Measured lifetimes of metastable levels of Mn X , Mn XI , Mn XII , and Mn XIII ions

An ion storage technique, based on the capture of metastable multiply charged ions from an external ion source into a Kingdon ion trap, has been used to measure the lifetimes of eight metastable levels of Mn ions with 3s3p configurations, k51 – 4. Although several lifetime calculations exist, some of the transition wavelengths have not been previously observed in any source. The lifetimes range...