Bent Functions, Partial Difference Sets, and Quasi-FrobeniusLocal Rings
Designs, Codes and Cryptography
q-ary Bent Functions Constructed from Chain Rings
Finite Fields and Their Applications
On the groups of units of finite commutative chain rings
Finite Fields and Their Applications
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A commutative ring with identity is called a chain ring if all its ideals form a chain under inclusion. A finite chain ring, roughly speaking, is an extension over a Galois ring of characteristic p^nusing an Eisenstein polynomial of degree k. When p@?k, such rings were classified up to isomorphism by Clark and Liang. However, relatively little is known about finite chain rings when p|k. In this paper, we allowed p|k. When n=2 or when p@?k but (p-1)@?k, we classified all pure finite chain rings up to isomorphism. Under the assumption that (p-1)@?k, we also determined the structures of groups of units of all finite chain rings.