This thesis consists of a summary part and seven published articles. All the articles are about performance analysis of ARQ schemes. Two of the publications study the performance of an ARQ scheme with packet combining, called the EARQ (extended ARQ) scheme. In the packet combining algorithm, the bitwise modulo-2 sum of two erroneous copies of a packet is computed to locate the errors. The packe...

We present the certifying part of the Zenon Modulo automated theorem prover, which is an extension of the Zenon tableau-based first order automated theorem prover to deduction modulo. The theory of deduction modulo is an extension of predicate calculus, which allows us to rewrite terms as well as propositions, and which is well suited for proof search in axiomatic theories, as it turns axioms i...

A polynomial ideal I ⊆ R[x] is THk-exact if every linear polynomial that is non-negative over VR(I), the real variety of I , is a sum of squares of polynomials of degree at most k modulo I . Lovász recognized that a graph is perfect if and only if the vanishing ideal of the characteristic vectors of its stable sets is TH1-exact, and asked for a characterization of ideals which are TH1-exact. We...

an ideal i of a ring r is called right baer-ideal if there exists an idempotent e 2 r such that r(i) = er. we know that r is quasi-baer if every ideal of r is a right baer-ideal, r is n-generalized right quasi-baer if for each i e r the ideal in is right baer-ideal, and r is right principaly quasi-baer if every principal right ideal of r is a right baer-ideal. therefore the concept of baer idea...

Let p > 3 be a prime, ζp a pth primitive root of 1, and ∆ the Galois group of Q(ζp) over Q. Let q 6= p be a prime and n the order of q modulo p. Assume q 6≡ 1 mod p and so n ≥ 2, p(q− 1)|qn − 1, and n|p− 1. Set f = (q − 1)/p and e = (p− 1)/n. Let Q be a prime ideal of Z[ζp] above q and let F = Z[ζp]/Q. Thus F ∼= Fqn , the finite field with q elements. Let α ∈ Z[ζp] be a generator of F such that...