数学专业人士翻译一下以下内容吧，要专业，急

Part IV ABSTRACT ALGEBRA 抽象代数学

4.1 Groups 群

4.1.1 Basic conceptions and judgments [subgroups, formal subgroups, quotient groups, cosets, index of subgroup, order of element, homomorphism, isomorphism, kernels] 4.1.2 Crucial examples [cyclic groups, permutation groups, linear groups]

4.1.3 Some simple calculations [order, index, cardinality of coset]

4.2 Rings

4.2.1 Basic conceptions and judgments [subrings, ideals, quotient rings, homomorphism, isomorphism, kernels]

4.2.2 Some qualified rings [integral rings (domains), commutative rings, rings equipped with a unit, and prime ideals, maximal ideals]

4.2.3 Crucial examples [rings of integrals, rings of algebraic numbers, rings of matrix]

4.3 Fields

4.3.1 Basic conceptions and judgments

4.3.2 Crucial examples [fields of numbers, finite fields Fp and their characteristics]

这是抽象代数学的内容，也是近代数学部分

4.1 群

4.1.1 基本概念与判断 [子集,正式子集,商群,陪集,子集索引,素的阶,同态,同形,核]

4.1.2 决定例 [循环群,排列群,线性群]

4.1.3 一些简单计算 [阶,索引,陪集的基数]

4.2 环

4.2.1 基本概念与判断 [子环,理想,商环,同态,同形,核]

4.2.2 一些合格环 [整数环(域),交换环,单元环,素(质)理想,极大理想]

4.2.3 关键例子 [积分环,代数数环,矩阵环]

4.3 域

4.3.1 基本概念与判断

4.3.2 关键例子 [数域,有限域Fp及其特性]