Commutative Chain Rings with Index of Nilpotency 5 and Residue Field <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula>
This paper gives a thorough characterization of chain rings with index of nilpotency 5 and residue field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="double-struck&q...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/13/12/877 |
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| Summary: | This paper gives a thorough characterization of chain rings with index of nilpotency 5 and residue field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>,</mo></mrow></semantics></math></inline-formula> where <i>p</i> represents a prime number, contributing valuable insights to the field of algebraic structures. It carefully identifies and categorizes the family of chain rings with these specifications, thereby enhancing the understanding of their properties and applications. In addition, the work offers a detailed enumeration of all chain rings containing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>p</mi><mrow><mn>5</mn><mi>m</mi></mrow></msup></semantics></math></inline-formula> elements. The significance of finite chain rings is emphasized, particularly in their suitability for coding theory, which confirms their relevance in contemporary mathematical and engineering contexts. |
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| ISSN: | 2075-1680 |