Finite Commutative Chain Ring Research Articles

New partial difference sets in p‐groups

AbstractLatin square type partial difference sets (PDS) are known to exist in R × R for various abelian p‐groups R and in ℤt. We construct a family of Latin square type PDS in ℤt × ℤ2ntp using finite commutative chain rings. When t is odd, the ambient group of the PDS is not covered by any previous construction. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 394–402, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10029

Exponent of a congruence-subgroup of a finite commutative chain ring

The exponent of a congruence-subgroup of the group of invertible matrices and the maximal order of an invertible matrix over the finite commutative wildly ramified chain ring are evaluated. This problem was previously considered in [1] where upper bounds for the exponent of a congruence-subgroup were derived.

Enumeration of finite commutative chain rings

A chain ring is an associative, commutative ring with an identity whose ideals form a chain. We associate with each finite chain ring five invariants (integers) and determine (in certain cases) the number of isomorphism classes of rings with given invariants. These results yield immediate corollaries for Pappian Hjelmslev planes which are coordinatized by such rings.