Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve recognizability, ge...

Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve rationality, genera...

in this paper, we introduce the concept of the   generalized aip-rings as a generalization of the generalized quasi-   baer rings   and generalized p.p.-rings. we show that the class of the generalized aip-rings is closed under direct products and morita invariance. we also characterize the 2-by-2 formal upper triangular matrix rings of this new class of rings. finally, we provide sever...

Blickle, Mustaţă and Smith proposed two conjectures on the limits of F-pure thresholds. One conjecture asks whether or not limit a sequence thresholds principal ideals regular local rings fixed dimension can be written as an thresshold in lower dimension. Another predicts that any threshold formal power series polynomial. In this paper, we prove first has counterexample but weaker statement sti...

Let K be the (real closed) field of Puiseux series in t over R endowed with the natural linear order. Then the elements of the formal power series rings R[[ξ1, . . . , ξn]] converge t-adically on [−t, t]n, and hence define functions [−t, t]n → K. Let L be the language of ordered fields, enriched with symbols for these functions. We show, in Corollary 3.17, that K is o-minimal in L. This result ...