algebras

简明释义

英[ˈæl.dʒə.brəz]美[ˈæl.dʒə.brəz]

n. [数]代数（algebra 的复数形式）

英英释义

单词用法

同义词

反义词

例句

1.As application, we give a equivalent axiom system of associative BCI-algebras.

作为应用，给出结合BCI -代数的一组等价公理系。

2.There are particular relations between the closed connected normal subgroups of algebraic groups and the ideals of Lie Algebras.

代数群的连通正规闭子群与李代数的理想之间有很特殊的关系。

3.We systematically sum up characteristics of advanced algebras in thought methods from the Angle of theory of knowledge.

从认识论的角度，系统地总结了高等代数在思想方法上的特点。

4.We study in this paper the structure of additive mappings on triangular matrix algebras which preserve commutativity.

本文研究了三角矩阵代数上保持交换性的可加映射的结构。

5.In the paper, we proved that every isomorphism of strohglyreducible triangular algebras is spatial.

本文证明了强可的极大三角代数的同构是空间实现的。

6.The complete constructions of scale generalized effect algebras and scale effect algebras are studied in this paper.

研究了标度广义效应代数与标度效应代数的代数结构，给出了比较完整的结果。

7.Many computer algorithms are based on principles from algebras 代数, particularly in data structures.

许多计算机算法基于algebras代数的原理，特别是在数据结构中。

8.Linear algebras 线性代数 are essential for solving systems of equations.

线性algebras线性代数对于解决方程组至关重要。

9.In advanced mathematics, we study different types of algebras 代数 to understand their properties.

在高级数学中，我们研究不同类型的algebras代数以理解它们的性质。

10.In physics, we often apply algebras 代数 to model complex systems.

在物理学中，我们经常应用algebras代数来建模复杂系统。

11.Abstract algebras 抽象代数 form the foundation of modern algebraic structures.

抽象algebras抽象代数构成了现代代数结构的基础。

作文

Algebra is one of the fundamental branches of mathematics, and it plays a crucial role in various fields, including science, engineering, and economics. Among its many forms, there are specific types known as algebras (代数), which extend the concepts of traditional algebra to more abstract structures. In this essay, I will explore the significance of algebras (代数) in mathematics and their applications in real-world scenarios.The term algebras (代数) refers to a collection of mathematical symbols and rules for manipulating these symbols. This area of study allows mathematicians to work with equations and functions in a more generalized way. One common type of algebras (代数) is linear algebra, which focuses on vector spaces and linear mappings between these spaces. Linear algebra is essential for understanding systems of linear equations, and it has applications in computer graphics, data science, and machine learning.Another important branch is abstract algebra, which deals with algebraic structures such as groups, rings, and fields. These structures provide a framework for understanding symmetry, number theory, and polynomial equations. The study of algebras (代数) in this context is vital for theoretical mathematics and has implications in cryptography, coding theory, and even quantum physics.In addition to pure mathematics, algebras (代数) have practical applications across various industries. For instance, in engineering, the principles of algebras (代数) are used to model and solve problems related to electrical circuits, structural analysis, and control systems. Engineers rely on these mathematical frameworks to ensure that their designs are efficient and effective.Moreover, in economics, algebras (代数) help economists create models that predict consumer behavior, market trends, and financial risks. By utilizing mathematical formulas and relationships, economists can analyze data and make informed decisions that impact businesses and governments alike.The significance of algebras (代数) also extends to computer science. Algorithms, which are step-by-step procedures for calculations, often rely on algebraic structures to function effectively. For example, data encryption methods use concepts from algebras (代数) to secure information, ensuring that sensitive data is protected from unauthorized access.Furthermore, educational institutions emphasize the importance of teaching algebras (代数) to students. A strong foundation in algebraic concepts is crucial for academic success in higher-level mathematics and science courses. Students who grasp the principles of algebras (代数) are better equipped to tackle complex problems and engage in critical thinking.In conclusion, algebras (代数) are an essential component of mathematics that influence numerous fields and applications. Their ability to generalize and abstract mathematical concepts allows for a deeper understanding of various phenomena in the world around us. As we continue to advance in technology and knowledge, the relevance of algebras (代数) will only grow, making it imperative for future generations to master these concepts. Whether in academia, industry, or everyday problem-solving, the study of algebras (代数) remains a cornerstone of modern mathematics.

代数是数学的基本分支之一，它在科学、工程和经济等各个领域中发挥着至关重要的作用。在其众多形式中，有一些特定类型被称为代数（algebras），它们将传统代数的概念扩展到更抽象的结构。本文将探讨代数（algebras）在数学中的重要性及其在现实世界中的应用。代数（algebras）这个术语指的是一组数学符号及其操作规则。这一研究领域使数学家能够以更一般化的方式处理方程和函数。一个常见的代数（algebras）类型是线性代数，它关注于向量空间及其之间的线性映射。线性代数对于理解线性方程组至关重要，并且在计算机图形学、数据科学和机器学习等领域中有着广泛的应用。另一个重要的分支是抽象代数，它处理群、环和域等代数结构。这些结构为理解对称性、数论和多项式方程提供了框架。在这种背景下，代数（algebras）的研究对理论数学至关重要，并在密码学、编码理论甚至量子物理中具有深远的影响。除了纯数学，代数（algebras）在各个行业中也有实际应用。例如，在工程学中，代数（algebras）的原理用于建模和解决与电路、结构分析和控制系统相关的问题。工程师依赖这些数学框架来确保他们的设计高效且有效。此外，在经济学中，代数（algebras）帮助经济学家创建模型，以预测消费者行为、市场趋势和金融风险。通过利用数学公式和关系，经济学家可以分析数据并做出影响企业和政府的明智决策。代数（algebras）的重要性还延伸到计算机科学。算法，即计算的逐步程序，通常依赖于代数结构才能有效运行。例如，数据加密方法使用来自代数（algebras）的概念来保护信息，确保敏感数据免受未经授权的访问。此外，教育机构强调教授代数（algebras）对学生的重要性。扎实的代数概念基础对于高年级数学和科学课程的学业成功至关重要。掌握代数（algebras）原则的学生更能应对复杂问题并参与批判性思维。总之，代数（algebras）是数学的一个重要组成部分，影响着众多领域和应用。它们将数学概念进行概括和抽象的能力，使我们能更深入地理解周围世界的各种现象。随着科技和知识的不断进步，代数（algebras）的相关性只会增加，因此未来几代人掌握这些概念显得尤为重要。无论是在学术界、工业界还是日常问题解决中，代数（algebras）的研究仍然是现代数学的基石。