l-adic (english) - meaning, definition, translation, pronunciation

Part of Speech

• Adjective

Phonetic Transcription

• /ɛl-ˈædɪk/

Meaning and Usage

The term "l-adic" relates to a system of mathematical constructs that extend the notion of integers in a specific way defined by a prime number ( l ). In mathematics, particularly in number theory, "l-adic" refers to a field of study characterized by the l-adic numbers, which are used for various purposes, such as studying Diophantine equations and other areas where distinct prime bases are involved. The use of "l-adic" is primarily in written contexts, especially in academic and research publications, mathematical texts, and during formal discussions in mathematics.

Example Sentences

1. "The study of l-adic numbers has revolutionized our understanding of number theory."
   "Изучение l-адических чисел произвело революцию в нашем понимании теории чисел."

2. "Using l-adic techniques, we can solve problems that were previously thought to be intractable."
   "Используя l-адические техники, мы можем решать проблемы, которые раньше считались неразрешимыми."

3. "The l-adic valuation provides insights into the structure of the integers."
   "l-адическая оценка дает понимание структуры целых чисел."

Idiomatic Expressions

"L-adic" does not have common idiomatic expressions in English, as it is primarily a technical term used in mathematics. However, in the context of mathematics, one can discuss broader expressions related to number theory that might occasionally incorporate the term.

• "Coming to grips with l-adic fields can be daunting for many mathematicians."
  "С пониманием l-адических полей может быть сложно для многих математиков."

• "The l-adic perspective opens new avenues in algebraic geometry."
  "l-адическая перспектива открывает новые пути в алгебраической геометрии."

Etymology

The term "l-adic" comes from "p-adic," which was introduced in the late 19th century in the context of number theory. The "l" denotes a particular prime number, similar to how "p" is used for a different prime. The term emphasizes the connection of this valuation system to a specific prime number.

Synonyms and Antonyms

• Synonyms: l-adic numbers, l-adic valuation
• Antonyms: There are no direct antonyms applicable as "l-adic" is a specific mathematical term without a contrasting use.

This collection of information provides a comprehensive overview of the term "l-adic" in its relevant mathematical context.