We partially answer two questions of Goodaire by showing that in a finite, strongly right alternative ring, the set of units (if the ring is with unity) is a Bol loop under ring multiplication, and the set of quasiregular elements is a Bol loop under " circle " multiplication. A magma (L, ·) is a set L with a binary operation · : L × L → L. A magma (L, ·) is a loop if there is a neutral element...

We show that two closed, connected $4$-manifolds with finite fundamental groups are $\mathbb{CP}^2$-stably homeomorphic if and only their quadratic $2$-types stably isomorphic Kirby-Siebenmann invariant agrees.

Let Λ be a left and right Artin ring and ΛωΛ a faithfully balanced selforthogonal bimodule. We give a sufficient condition that the injective dimension of ωΛ is finite implies that of Λω is also finite.  2003 Elsevier Science (USA). All rights reserved.

Let R be a ring and T be a 1-tilting right R-module. Then T is of countable type. Moreover, T is of finite type in case R is a Prüfer domain.

By means of a kind of new idea, we redefine some kinds of fuzzy ideals in a ring and investigate some of their related properties. The concepts of strong prime (semiprime) generalized fuzzy (bi-, quasi-) ideals in rings are introduced. In particular, we discuss the relationships between strong prime (resp., semiprime) generalized fuzzy (bi-, quasi-) ideals and prime (resp. semiprime) generalize...

A ghost in the stable module category of a group G is a map between representations of G that is invisible to Tate cohomology. We show that the only non-trivial finite p-groups whose stable module categories have no non-trivial ghosts are the cyclic groups C2 and C3. We compare this to the situation in the derived category of a commutative ring. We also determine for which groups G the second p...

Let k be a field of finite characteristic p, and G a finite group acting on the left on a finite dimensional k-vector space V . Then the dual vector space V ∗ is naturally a right kG-module, and the symmetric algebra of the dual, R := Sym(V ∗), is a polynomial ring over k on which G acts naturally by graded algebra automorphisms, and if k is algebraically closed can be regarded as the space k[V...

In this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $Z_{2}$. We also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

A ring $R$ with an automorphism $sigma$ and a $sigma$-derivation $delta$ is called $delta$-quasi-Baer (resp., $sigma$-invariant quasi-Baer) if the right annihilator of every $delta$-ideal (resp., $sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let $A=sigma(R)leftlangle x...

We study the relation (and differences) between stability and Property (S) in simple stably finite framework. This leads us to characterize stable elements terms of their support, these concepts from different sides: hereditary subalgebras, projections multiplier algebra order properties Cuntz semigroup. use approaches show both that cancellation at infinity on semigroup just holds when its equ...