In modular 4 residue class rings, irreversible elements refer to elements without inverse elements under multiplication operation. In this ring, only the elements 1 and 3 are reversible because their product is still 1. Elements 0 and 2 are irreversible because their product is still 0. Therefore, there are two irreversible elements in the residual class ring of module 4.

The modular method of calculating z: let the complex number z be equal to a plus bi. Complex modulus in mathematics. The value of the positive square root of the sum of the squares of the real and imaginary parts of a complex number is called the module of the complex number. Its geometric meaning is the distance from a point on the complex plane to the origin. The concept of plane: plane has no thickness; The plane area cannot be measured; The plane extends infinitely; A straight line in the plane divides the plane into two parts; A plane divides the space into two parts.

The residue class ring of module m R= residue class of module M} specifies that the addition and multiplication in r are as follows: [a+b]=[a+6[al[b=[ab].

Fully correct the attitude towards mathematics and fully realize the importance of mathematical practice. Practice can not only improve the answering speed and master the answering skills, but also often lead to many new problems in practice.

Many mathematical objects, such as numbers, functions, geometry, etc., reflect the internal structure of continuous operation or the relationships defined therein. Mathematics studies the properties of these structures, for example, number theory studies how integers are represented under arithmetic operations. In addition, similar things often happen in different structures, which is further abstract.

For example, some old problems in ruler drawing were finally solved by Galois theory, which involves domain theory and group theory. Another example of algebraic theory is linear algebra, which makes a general study of vector spaces with quantitative and directional elements. These phenomena show that geometry and algebra, which were originally considered irrelevant, actually have a strong correlation. Combinatorial mathematics studies the method of enumerating several objects satisfying a given structure.