Let R be a ring and S a nonempty subset of R. Suppose that θ and φ are endomorphisms of R. An additive mapping δ : R → R is called a left (θ,φ)-derivation (resp., Jordan left (θ,φ)derivation) on S if δ(xy) = θ(x)δ(y)+φ(y)δ(x) (resp., δ(x2) = θ(x)δ(x)+φ(x)δ(x)) holds for all x,y ∈ S. Suppose that J is a Jordan ideal and a subring of a 2-torsion-free prime ring R. In the present paper, it is show...

If R is a commutative unital ring and M R-module, then each element of EndR(M) determines left EndR(M)[X]-module structure on EndR(M), where the R-algebra endomorphisms EndR(M)[X]=EndR(M)⊗RR[X]. These structures provide very short proof Cayley-Hamilton theorem, which may be viewed as reformulation in Algebra by Serge Lang. Some generalisations theorem can easily proved using proposed method.

In this paper, the endomorphisms, the half-strong endomorphisms, the locally strong endomorphisms, the quasi-strong endomorphisms, the strong endomorphisms and the automorphisms of a join of cycle n C and a vertex y are investigated. Some enumerative problems concerning these graphs are solved. In particular, the endomorphism spectrums and the endomorphism types of these graphs are given. It ha...

We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This provides a purely categorical proof of a conjecture by Ostrik concerning the structure of F . As a by-product we obtain a concrete expression for the structure...

We apply minimal weakly generating sets to study the existence of Add ( U R ) -covers for a uniserial module . If is right over ring , then S : = End has at most two maximal (right, left, two-sided) ideals: one set I all endomorphisms that are not injective, and other K surjective. prove if either finitely generated, or artinian, ? class covering only it closed under direct limit. Moreover, we ...

Let B be a unital commutative semi-simple Banach algebra. We study endomorphisms of B which are simultaneously Riesz operators. Clearly compact and power compact endomorphisms are Riesz. Several general theorems about Riesz endomorphisms are proved, and these results are then applied to the question of when Riesz endomorphisms of certain algebras are necessarily power compact.

has only trivial endomorphisms over an algebraic closure of the ground field K if the Galois group Gal(f) of the polynomial f ∈ K[x] is “very big”. More precisely, if f is a polynomial of degree n ≥ 5 and Gal(f) is either the symmetric group Sn or the alternating group An then End(J(C)) = Z. Notice that it easily follows that the ring of K-endomorphisms of J(C) coincides with Z and the real pro...

Let $K$ be a field of prime characteristic $p$, $n>4 $ an integer, $f(x)$ irreducible polynomial over degree $n$, whose Galois group is either the full symmetric $S_n$ or alternating $A_n$. $l$ odd different from $Z[\zeta_l]$ ring integers in $l$th cyclotomic field, $C_{f,l}:y^l=f(x)$ corresponding superelliptic curve and $J(C_{f,l})$ its jacobian. We prove that all endomorphisms coincides with...

On the commuting polynomial endomorphisms of C 2 We determine all couples of commuting polynomial endomorphisms of C 2 that extends to holomorphic endomorphisms of P 2 and that have disjoint sequences of iterates.