let $mathbb{f}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted lie superalgebra over $mathbb{f}$. it is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. these quotient superalgebras are called the generalized reduced enveloping ...

A skew generalized power series ring R[[S, ω]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action ω of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are...

Let K be a field of characteristic zero and let K((R≤0)) denote the ring of generalized power series (i.e., formal sums with well-ordered support) with coefficients in K, and non-positive real exponents. Berarducci (2000) constructed an irreducible omnific integer, in the sense of Conway (2001), by first proving that an element of K((R≤0)) that is not divisible by a monomial and whose support h...

A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol’s result, we prove that the same assertion holds for generalized power series (whose index sets may be arbitrary well-ordered sets of nonnegative rationals).

We resolve an open problem in commutative algebra and Field Arithmetic, posed by Jarden – Let R be a generalized Krull domain. Is the ring R[[X]] of formal power series over R a generalized Krull domain? We show that the answer is negative.