IN THIS PAPER, WE INTRODUCE THE SMALLEST EQUIVALENCE relation V* ON A HYPERGROUP H SUCH THAT THE QUOTIENT H/V*, THE SET OF ALL EQUIVALENCE CLASSES, IS A NILPOTENT GROUP.

Introduction: Diabetes is a metabolic disorder that produced by low secretion of insulin or resistant to insulin. Oxidative stress is an imbalance between the free radical production and antioxidant defense systems of the body and strongly related with diabetes and symptoms of it. Swimming exercise via enhancing antioxidant defenses can decrease the symptoms of diabetes.Methods: Diabetes was produced by streptozotocin (STZ, i.p injection, single dose, 50mg/Kg). Duration of exercise was 8 weeks. At the end of experiments, the rats were anesthetized by ether and the heads cut by guillotine, brain removed and hippocampus of brain was removed on ice immediately. Tissue was homogenized in prepared buffer and after sentrifusion produced supernatant was used for determination of SOD, GPX and CAT activities, and MDA level.Results: Diabetes reduced SOD activity and GPX of hippocampus in diabetic rats significantly. MDA level increased in diabetic rats significantly compared with control. In response to exercise MDA level decreased in diabetic rats and SOD activity, GPX and catalase activity increased significantly.Conclusion: Swimming exercise by increasing of hippocampus antioxidant enzymes and decreasing of MDA level has beneficial effects in prevention the neurotic symptoms of diabetes mellitus and tissue injuries by oxidative stress produced by this disease.

WE INTRODUCE TWO EQUIVALENCE relationS ON SEMIHYPERGROUPS. ALSO WE DISCUSS ON SOME PROPERTIES OF THESE TWO relationS AND INVESTIGATE ON QUOTIENT SEMIHYPERGROUPS VIA THESE relationS.

ONE OF THE MOST IMPORTANT TOOLS IN ALGEBRAIC (M, N) -HYPERSTRUCTURES IS REPRESENTED BY STRONGLY regular relationS, WHICH CONNECTS AN ALGEBRAIC (M, N) -HYPERSTRUCTURE TO THE ASSOCIATED ALGEBRAIC (M, N) -STRUCTURE. IN THIS PAPER, WE DEFINE THE NOTION OF A NORMAL HYPERIDEAL FOR A KRASNER (M, N) -HYPERRING AND SHOW THAT IT HAS A BEHAVIOR SIMILAR TO STRONGLY regular relationS AND WE CAN OBTAIN TRIVIAL KRASNER (M, N) -HYPERRINGS BY IT.