On rings whose flat modules form a Grothendieck category
On rings with a unique proper essential right ideal
Right ue-rings (rings with the property of the title, i.e., with the maximality of the right socle) are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a regular V-ring with the socle being a maximal right ideal, and if and only if the intrinsic topology of R is non-discrete Hausdorff and dense proper right ideals are semisimple. It is proved that if R is a right self-injective right ue-ring (local right ue-ring), then R is never semiprime and is Artin semisimple...
On Rings with Polynomial Identity xn-x=0
On rings with prime centers.
On rings with zero divisors. Strong -groups
On rings with zero total.
On Roth's pseudo equivalence over rings.
On -Noetherian rings
Let be a commutative ring and a given multiplicative set. Let be a strictly ordered monoid satisfying the condition that for every . Then it is shown, under some additional conditions, that the generalized power series ring is -Noetherian if and only if is -Noetherian and is finitely generated.
On selfinjective algebras of Euclidean type
On self-injective algebras of finite representation type
We describe the structure of finite-dimensional self-injective algebras of finite representation type over a field whose stable Auslander-Reiten quiver has a sectional module not lying on a short chain.
On selfinjective algebras of tilted type
We provide a characterization of all finite-dimensional selfinjective algebras over a field K which are socle equivalent to a prominent class of selfinjective algebras of tilted type.
On selfinjective algebras without short cycles in the component quiver
We give a complete description of all finite-dimensional selfinjective algebras over an algebraically closed field whose component quiver has no short cycles.
On selfinjective artin algebras having nonperiodic generalized standard Auslander-Reiten components
We describe the structure of all selfinjective artin algebras having at least three nonperiodic generalized standard Auslander-Reiten components. In particular, all selfinjective artin algebras having a generalized standard Auslander-Reiten component of Euclidean type are described.
On semiabelian -regular rings.
On semifir monoid rings.
We give a new condition on a monoid M for the monoid ring F[M] to be a 2-fir. Furthermore, we construct a monoid M that satisfies all the currently known necessary conditions for F[M] to be a semifir and that the group of units of M is trivial, but M is not a directed union of free monoids.
On semigroup algebras satysfying polynomial identities.
On semigroup graded PI-algebras.
On semigroup rings.
On semi-invariants of tilted algebras of type Aₙ
We prove that for algebras obtained by tilts from the path algebras of equioriented Dynkin diagrams of type Aₙ, the rings of semi-invariants are polynomial.
On semiprime twisted semigroup rings.