Primitive idempotents and constacyclic codes over finite chain rings

Charkani, Mohammed Elhassani; Kaboré, Joël

doi:10.56947/gjom.v8i2.434

Cited by 3 publications

(1 citation statement)

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“…As explained above, part of this article is intended to study rings that are not necessarily commutative in the spirit of some of the chain-theoretic work in [11]. We would hope that some readers of this journal would be especially interested in examining whether the code-theoretic work on certain finite commutative rings in [4] and/or the graph-theoretic work that had applications to certain finite commutative rings in [30] could also be extended to contexts involving some noncommutative rings.…”

Section: Introductionmentioning

confidence: 99%

On minimal ring extensions of finite rings

Dobbs

2022

GJOM

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Two conditions, (i) and (ii), are defined, that may hold for a given (unital) ring extension R ⊂ S of (unital, associative, not necessarily commutative) finite rings. It is shown that if S is commutative, then ``"either (i) or (ii)” is a necessary and sufficient condition for R ⊂ S to be a minimal ring extension; and that for such extensions, (i) and (ii) are logically independent. For extensions with S (finite and) noncommutative, "either (i) or (ii)” is neither necessary nor sufficient for R ⊂ S to be a minimal ring extension; and for such minimal ring extensions, (i) and (ii) are logically independent. Next, let R ⊂ Sj be minimal ring extensions with Sj (finite and) commutative (for j=1,2) and R local. Then: S1 and S2 are the same type (that is, ramified, decomposed or inert) of minimal extension of R ↔ |Z(S_1)|=|Z(S_2)| ↔ |U(S_1)|=|U(S_2)|.

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Section: Introductionmentioning

confidence: 99%