同构定理 meaning in English

isomorphism theorems

In first section , the concept of pseudo ideal is raised . then , we discuss the relations of pseudo ideals , kernel of homomorphisms and congruences on a division semiring . and the homomorphic basic theorem , the first and the second isomorphic theorems are proved
第一部分，引入伪理想这一新概念，讨论了伪理想，同态核，同余在可除半环中的关系，证明了同态基本定理及第一、二同构定理
In the second section , we structure a kind of semirings , namely semidirect product of semirings , and prove an isomorphic theorem of semidirect products . in the third section , we give the characterizations of the relations of all kinds of regular semirings and introduce the concept of pseudo - inverse and the necessary and sufficient conditions of pseudo - invertible element . in the fourth section , we define an equivalence relation on the cartersian product of commutative semiring and its multiplicative subset
第二部分，先构造一类半环，半环半直积，然后证明半直积的同构定理第三部分，刻划了半环各类正则元之间关系，引入伪逆的定义，给出了可伪逆元素的充要条件第四部分，在交换半环和乘法集的卡氏积上定义等价关系，进而构造了一类交换半环：分式半环