The PVS theory includes complete proofs of the three classical isomorphism theorems for rings, and characterizations of principal, prime and maximal ideals. Algebraic concepts and properties are specified and formalized as generally as possible allowing in this manner their application to other algebraic ...
It is proved that there is a collineation between two octonion planes over local rings if and only if the underlying octonion algebras are isomorphic as rings. It is shown that every isomorphism between the little or middle projective groups of two octonion planes over local rings is induced by...
On Mal’cev type theorems on elementary equivalences of linear groups and rings of matrices; 8. Related topics; 8.1. Representation of rings as full matrix rings (hidden matrices); 8.2. Isomorphisms and automorphisms of triangular and ... AV Mikhalev 被引量: 14发表: 1996年 ...
This follows readily from the isomorphism theorems for rings. en.wikipedia.org It is an -category generalization of a groupoid, a category in which every morphism is an isomorphism. en.wikipedia.org However, the isomorphism theorem gives a stronger result, because ring isomorphisms preserve multipl...
摘要: The three isomorphism theorems of ring theory are derived in the context of hyperrings. Then a Jordan-Hlder theorem is derived for hyperrings. Finally, we consider the fundamental relation γ * defined on a hyperring and prove some results and a fundamental theorem in this respect....
On Mal’cev type theorems on elementary equivalences of linear groups and rings of matrices; 8. Related ... AV Mikhalev 被引量: 14发表: 1996年 The first and second fundamental theorems of invariant theory for the quantum general linear supergroup We develop the non-commutative polynomial ...
In [1], we encoded some theorems concerning the product of cyclic groups. In this article, we present the generalized formalization of [1]. First, we show that every finite commutative... H Okazaki,H Yamazaki,Y Shidama - 《Formalized Mathematics》 被引量: 6发表: 2013年 Statistics of ...
Fuzzy Isomorphism Theorems of Hyperrings超环的模糊同构定理 超环正规模糊超理想同构.The concept of normal fuzzy hyperideals of hyperrings is introduced and then some fuzzy isomorphism theorems of hyperrings is obtained by normal fuzzy hyperideals.马学玲詹建明系统科学与数学...
Zhan, Fuzzy isomorphism the- orems of soft rings, Neural Comput. Appl. 21(2012) 391-397.X. Liu, D. Xiang, and J. Zhan, "Fuzzy isomorphism theorems of soft rings," Neural Computing and Applications, vol. 21, no. 2, pp. 391-397, 2012....
Recently, Krasner ( m , n )-hyperrings were introduced and analyzed by Davvaz et. al. This is a suitable generalization of Krasner hyperrings. In this research work, we consider that if I is a normal hyperideal of a Krasner ( m , n )-hyperring R , then the quotient hyperring [ ...