给出了弱t -余代数的定义，构造了其上的模结构。
The definition of weak T-coalgebra is given and modules over it is constructed.
第二部分研究了代数与余代数之间的缠扭结构以及与其密切相关的代数分解理论。
In Part Two we study the theory of entwining structures and that of factorization structures.
通过研究双对称代数的对偶结构，主要讨论双对称余代数的张量积及双对称代数和双对称余代数之间的对偶关系。
The tensor products of double-symmetric coalgebras and the dual relationships between double-symmetric algebras and double-symmetric coalgebras are discussed.
第二步，我们要找另一个矩阵，叫代数余子式。
在高等代数教课书中，关于多项式的除法运算中余项的确定是以余式定理为依据且利用带余除法进行的，这是大家所熟悉的。
In the textbook of higher algebra, it is familiar to us that the remainder in the division operation of polynomial is on the basis of residue theorem and operated through division algorithm.
利用BCI -代数的固有理想这一概念，在BCI -代数中定义了一个同余关系，从而得到这个BCI -代数的固有商代数。
In a BCI-algebra, a congruence relation is defined by using its intrinsic ideal, thus the intrinsic quotient algebra of the BCI -algebra is obtained.
利用半代数的同余来讨论半代数的同态定理及其第一，第二同构定理。
Then, with congruence of the semialgebra, we proved the homomorphic theorem of semialgebra and its first and second isomorphic theorems.
从双代数的定义入手，给出了双代数成为交换和余交换双代数的两个充分条件。
We study the definition of bialgebra and prove the sufficient conditions about a bialgebra is commutative and cocommutative.
基于矩阵多元多项式的带余除法，给出了代数情形多项式组特征列的一种新求法，并举例验证了这种方法的有效性。
Based on the pseudo-division algorithm for multivariate matrix polynomials, a new solving process of characteristic series for algebraic polynomial systems is given.
借助近似代数上的原子及同余关系，证明了在适当选取余运算之后，粗集代数就构成伪补MS代数。
Based on the atoms and congruence relations of approximation algebra, it is proved that rough set algebra becomes pseudo-complemented ms algebra if proper complement operators are selected.
本文提出伪补MS-代数（简称PMS-代数）中正则理想，正则同余关系等概念。
In this paper, we introduce notions of regular ideals of a pseudocomplemented MS-algebra (PMS-algebra, for short) and study their elementary properies.
给出有关代数余子式之和的几个性质并予以证明，且给出利用代数余子式之和计算行列式的方法。
This paper elaborates several features of the sum of the cofactor of a determinant and provides the method to calculate the determinant of a Matrix by the sum of the cofactor of a determinant.
在一元泛代数上引入了双同余关系，从而使双同态映射与双同构映射得到了沟通。
In this paper we have given the concept of double-congruence, by which the concepts of double-homomorphism and double-isomorphism in a unary algebra are linked together.
给出了三种代数类具有可定义主同余性质的证明。
This article mainly gives three kinds of algebra classes which have the property of definable principal congruence and their verifications.
本文的另一个结果是获得了求节点导纳矩阵任意一个二阶代数余子式的拓扑公式。
Another result is presented a topological formula for any 2-order algebraic cofactor in passive network node admittance matrixes.
本文的另一个结果是获得了求节点导纳矩阵任意一个二阶代数余子式的拓扑公式。
Another result is presented a topological formula for any 2-order algebraic cofactor in passive network node admittance matrixes.
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