TY  - JOUR
T1  - Necessary and Sufficient Conditions Where One Γ-Semigroup is a Γ-Group
AU - Sadiku, Sabri 
JO  - Journal of Modern Mathematics and Statistics
VL  - 4
IS  - 1
SP  - 44
EP  - 49
PY  - 2010
DA  - 2001/08/19
SN  - 1994-5388
DO  - jmmstat.2010.44.49
UR  - https://makhillpublications.co/view-article.php?doi=jmmstat.2010.44.49
KW  - ±-idempotent element
KW  -(±
KW  - ²)-inverse element
KW  -“-semigroups
KW  -“-algebraic structures
KW  -“-semigroup idempotent
KW  -“-group
AB  - In this study, researchers have studied the Γ-algebraic structures and some characteristics of them. According to Sen and Saha, we defined algebraic structures: Γ-semigroup, Γ-regular semigroup, Γ-idempotent semigroup, Γ-invers semigroup and Γ-group. Theorem 2, 3 and 4 proves the existence of Γ-group and gives necessary and sufficient conditions where one Γ-semigroup is a Γ-group. Finally, theorem 5 shows necessary and sufficient conditions where one Γ-regular semigroup is a Γ-group. In addition, for every Γ- algebraic structure that we mentioned before we give an original example.
ER  -