On Krull dimension of Ore extensions.
In this paper we extend the concept of an -fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring , and we show that each level left (resp. right) ideal of an -fuzzy left (resp. right) ideal of is characteristic iff is -fuzzy characteristic.
We study some properties of -fuzzy left (right) ideals of a semiring related to level left (right) ideals.
We construct non faithful direct summands of tilting (resp. cotilting) modules large enough to inherit a functorial tilting (resp. cotilting) behaviour.
Let be a -torsion free prime ring. Suppose that are automorphisms of . In the present paper it is established that if admits a nonzero Jordan left -derivation, then is commutative. Further, as an application of this resul it is shown that every Jordan left -derivation on is a left -derivation on . Finally, in case of an arbitrary prime ring it is proved that if admits a left -derivation which acts also as a homomorphism (resp. anti-homomorphism) on a nonzero ideal of , then ...
In a manner analogous to a commutative ring, the L-ideal-based L-zero-divisor graph of a commutative ring R can be defined as the undirected graph Γ(μ) for some L-ideal μ of R. The basic properties and possible structures of the graph Γ(μ) are studied.
The category of group-graded modules over an abelian group is a monoidal category. For any bicharacter of this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have -ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative...
Let be a 2-torsion free prime ring and let be a Lie ideal of such that for all . In the present paper it is shown that if is an additive mappings of into itself satisfying for all , then for all .
Starting with some observations on (strong) lifting of idempotents, we characterize a module whose endomorphism ring is semiregular with respect to the ideal of endomorphisms with small image. This is the dual of Yamagata's work [Colloq. Math. 113 (2008)] on a module whose endomorphism ring is semiregular with respect to the ideal of endomorphisms with large kernel.
Let be the general Boolean algebra and a linear operator on . If for any in (, respectively), is regular (invertible, respectively) if and only if is regular (invertible, respectively), then is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over . Meanwhile, noting that a general Boolean algebra is isomorphic...
Let k be a field. We prove that any polynomial ring over k is a Kadison algebra if and only if k is infinite. Moreover, we present some new examples of Kadison algebras and examples of algebras which are not Kadison algebras.
Let Λ = (S/R,α) be a local weak crossed product order in the crossed product algebra A = (L/K,α) with integral cocycle, and the inertial group of α, for S* the group of units of S. We give a condition for the first ramification group of L/K to be a subgroup of H. Moreover we describe the Jacobson radical of Λ without restriction on the ramification of L/K.