Rationally Additive Semirings
نویسندگان
چکیده
We define rationally additive semirings that are a generalization of (ω)complete and (ω-)continuous semirings. We prove that every rationally additive semiring is an iteration semiring. Moreover, we characterize the semirings of rational power series with coefficients in N∞, the semiring of natural numbers equipped with a top element, as the free rationally additive semirings.
منابع مشابه
Distributive Lattices of λ-simple Semirings
In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left $k$-radicals $Lambda(a)={x in S | a stackrel{l}{longrightarrow^{infty}} x}$ induced by the transitive closure $stackrel{l}{longrightarrow^{infty}}$ of the relation $stackrel{l}{longrightarrow}$ which induce the equivalence relation $lambda$. Again non-transit...
متن کاملKleene Algebra
3 Dioids 4 3.1 Join Semilattices . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Join Semilattices with an Additive Unit . . . . . . . . . . . . 5 3.3 Near Semirings . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Variants of Dioids . . . . . . . . . . . . . . . . . . . . . . . . 6 3.5 Families of Nearsemirings with a Multiplicative Unit . . . . . 8 3.6 Families of Nearsemirin...
متن کاملSemirings whose additive endomorphisms are multiplicative
A ring or an idempotent semiring is associative provided that additive endomorphisms are multiplicative.
متن کاملar X iv : 1 10 8 . 28 74 v 1 [ m at h . Q A ] 1 4 A ug 2 01 1 THERMODYNAMIC SEMIRINGS
Thermodynamic semirings are deformed additive structures on characteristic one semirings, defined using a binary information measure. The algebraic properties of the semiring encode thermodynamical and information theoretic properties of the entropy function. Besides the case of the Shannon entropy, which arises in the context of geometry over the field with one element and the Witt constructio...
متن کاملCircuit Evaluation for Finite Semirings
The computational complexity of the circuit evaluation problem for finite semirings is considered, where semirings are not assumed to have an additive or multiplicative identity. The following dichotomy is shown: If a finite semiring is such that (i) the multiplicative semigroup is solvable and (ii) it does not contain a subsemiring with an additive identity 0 and a multiplicative identity 1 6=...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. UCS
دوره 8 شماره
صفحات -
تاریخ انتشار 2002