‎let $mathcal a$ and $mathcal b$ be unital rings‎, ‎and $mathcal m$‎ ‎be an $(mathcal a‎, ‎mathcal b)$-bimodule‎, ‎which is faithful as a‎ ‎left $mathcal a$-module and also as a right $mathcal b$-module‎. ‎let ${mathcal u}=mbox{rm tri}(mathcal a‎, ‎mathcal m‎, ‎mathcal‎ ‎b)$ be the triangular ring and ${mathcal z}({mathcal u})$ its‎ ‎center‎. ‎assume that $f:{mathcal u}rightarrow{mathcal u}$ is...

‎Let $mathcal A$ and $mathcal B$ be unital rings‎, ‎and $mathcal M$‎ ‎be an $(mathcal A‎, ‎mathcal B)$-bimodule‎, ‎which is faithful as a‎ ‎left $mathcal A$-module and also as a right $mathcal B$-module‎. ‎Let ${mathcal U}=mbox{rm Tri}(mathcal A‎, ‎mathcal M‎, ‎mathcal‎ ‎B)$ be the triangular ring and ${mathcal Z}({mathcal U})$ its‎ ‎center‎. ‎Assume that $f:{mathcal U}rightarrow{mathcal U}$ is...

We introduce (k, l)-regular maps, which generalize two previously studied classes of maps: affinely k-regular maps and totally skew embeddings. We exhibit some explicit examples and obtain bounds on the least dimension of a Euclidean space into which a manifold can be embedded by a (k, l)-regular map. The problem can be regarded as an extension of embedding theory to embeddings with certain non...

Let A be a non-commutative prime ring with involution ∗, of characteristic ≠2(and3), Z as the center and Π mapping Π:A→A such that [Π(x),x]∈Z for all (skew) symmetric elements x∈A. If is non-zero CE-Jordan derivation A, then satisfies s4, standard polynomial degree 4. ∗-derivation s4 or Π(y)=λ(y−y*) y∈A, some λ∈C, extended centroid A. Furthermore, we give an example to demonstrate importance re...

We study certain properties of derivations on semiprime rings. The main purpose is to prove the following result: let R be a semiprime ring with center Z(R), and let f , g be derivations of R such that f(x)x+xg(x) ∈ Z(R) for all x ∈ R, then f and g are central. As an application, we show that noncommutative semisimple Banach algebras do not admit nonzero linear derivations satisfying the above ...

Let G be a finite group and H a normal subgroup such that G/H is cyclic. Given a conjugacy class g of G we define its centralizing subgroup to be HCG(g). Let K be such that H ≤ K ≤ G. We show that the G-conjugacy classes contained in K whose centralizing subgroup is K, are equally distributed between the cosets of H in K. The proof of this result is entirely elementary. As an application we fin...