Visualizing the Group Homomorphism Theorem

1995 ◽  
Vol 26 (2) ◽  
pp. 143
Author(s):  
Robert C. Moore
2011 ◽  
Vol 46 (9) ◽  
pp. 385-391
Author(s):  
Shin-Cheng Mu ◽  
Akimasa Morihata

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 321 ◽  
Author(s):  
Mehmet Çelik ◽  
Moges Shalla ◽  
Necati Olgun

In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related.


2005 ◽  
Vol 5 (4) ◽  
pp. 1315-1324 ◽  
Author(s):  
Teruaki Kitano ◽  
Masaaki Suzuki ◽  
Masaaki Wada

1967 ◽  
Vol 19 ◽  
pp. 419-426 ◽  
Author(s):  
R. J. Warne

A bisimple semigroup S is called I-bisimple if Es, the set of idempotents of S, with its natural order is order-isomorphic to I, the set of integers, under the reverse of the usual order. In (9), the author completely determined the structure of I-bisimple semigroups mod groups; in this paper, he also gave an isomorphism theorem, a homomorphism theorem, an explicit determination of the maximal group homomorphic image, and a complete determination of the congruences for these semigroups.


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