Pencils of Higher Derivations of Arbitrary Field Extensions

Pencils of Higher Derivations of Arbitrary Field Extensions

Let L be a field of characteristic p ^ 0. A subfield K of L is Galois if A' is the field of constants of a group of pencils of higher derivations on L. Let F d K be Galois subfields of L. Then the group of L over F is a normal subgroup of the group of L over K if and only if F = K(W') for some nonnegative integer r. If L/K splits as the tensor product of a purely inseparable extension and a sep...

Higher Derivations and Field Extensions

Let K be a field having prime characteristic p. The following conditions on a subfield k of K are equivalent: (i) || K" (k) = k and K/k is separable, (ii) k is the field of constants of an infinite higher derivation defined in K. (iii) k is the field of constants of a set of infinite higher derivations defined in K. If K/k is separably generated and k is algebraically closed in K, then k is the...

Galois Theory for Arbitrary Field Extensions

Local higher derivations on C*-algebras are higher derivations

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

extensions, minimality and idempotents of certain semigroup compactifications

در فصل اول مقدمات و پیش نیازهای لازم برای فصل های بعدی فراهم گردیده است . در فصل دوم مساله توسیع مورد توجه قرار گرفته و ابتدا شرایطی که تحت آن از یک فشرده سازی نیم گروهی خاص یک زیرگروه نرمال بسته یک گروه به یک فشرده سازی متناظر با فشرده سازی اولیه برای گروه رسید مورد بررسی قرار گرفته و سپس ارتیاط بین ساختارهای مختلف روی این دو فشرده سازی از جمله ایده آل های مینیمال چپ و راست و... مورد بررسی قرا...