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Some Remarks on Rings

100%

Obojska L., O’Hara P.

Commentationes Mathematicae

2010

tom 50

nr 1

Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and \(\sigma\)-Fields are well known and much has been written about them. In this paper we explore some properties of rings related to the distribution law. Specifically, we shall show that for rings there exists only one distribution law. Moreover, for the ring \((Z_{p(p−1)n} +, \cdot)\), where \((p, n) = 1\) there exist isomorphic groups \((G, +)\), \((H, \cdot)\), \(G, H \subset Z_{p(p−1)n}\) of the order \((p − 1)\). Finally, we note that every ring \((Z_{pn}, +, \cdot)\) contains subfields \(\text{mod}(pn)\).

The isomorphism relation between tree-automatic Structures

63%

Finkel O., Todorčević S.

Open Mathematics

2010

tom 8

nr 2

299-313

An ω-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for ω-tree-automatic structures. We prove first that the isomorphism relation for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is neither a Σ21-set nor a Π21-set.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Open Mathematics

1 Finkel O.

1 Obojska L.

1 O’Hara P.

1 Todorčević S.

2 2010

Wyniki wyszukiwania

Some Remarks on Rings

The isomorphism relation between tree-automatic Structures