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Register a new userOn the decidability of the theory of modules over the ring of algebraic integers
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We prove that the theory of all modules over the ring of algebraic integers is decidable.
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We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prufer (in particular Bezout) domains with infinite residue fields in terms of a suitable generalization of the prime radical relation. For B{e}zout domains these conditions are also necessary.
We show that K_{2i}(Z[x,y]/(xy),(x,y)) is free abelian of rank 1 and that K_{2i+1}(Z[x,y]/(xy),(x,y)) is finite of order (i!)^2. We also compute K_{2i+1}(Z[x,y]/(xy),(x,y)) in low degrees.
We show that the K_{2i}(Z[x]/(x^m),(x)) is finite of order (mi)!(i!)^{m-2} and that K_{2i+1}(Z[x]/(x^m),(x)) is free abelian of rank m-1. This is accomplished by showing that the equivariant homotopy groups of the topological Hochschild spectrum THH(Z) are finite, in odd degrees, and free abelian, in even degrees, and by evaluating their orders and ranks, respectively.
In this paper we give a Casimir Invariant for the Symmetric group $S_n$. Furthermore we obtain and present, for the first time in the literature, explicit formulas for the matrices of the standard representation in terms of the matrices of the permutation representation.
We solve the decidability problem for Boolean Set Theory with unordered cartesian product.
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