Some Characterizations of Nil Ideals in BCI—algebras

51.IntrodcutionIn[1j,thenotionsofnilidealinBCI-algebrasandinlBCI-algebrawereintreduced.WeshowthatnilBCI-algebraisageneralizationofassociativeandquasi-associativeBCIalgebra([2J,[3j).lnthispaper,somecharacterizationsofnilidealsinBCI-algebraswereproved.Moreover,theBCI-algebrassatifyingO*x.=xwerediscussedandvariousproPertieswereproved.Werecallsomedefinitionsande1ementaryproperties.ThefollowingsaretrueinaBCI-al-gebra:(l)x o=x;(2)(x*y)*z=(x z) y;(3)x相似文献   

相关系的子相关系

在相关系概念的基础上,建立了相关系的子相关系,并进行了初步探究,得到了子相关系的若干性质.     

The Semigroup Characterizations of Positive Implicative BCK—algebras

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＢｙａＢＣＩ－ａｌｇｅｂｒａｗｅｍｅａｎａｎａｌｇｅｂｒａ（Ｘ，，０）ｏｆｔｙｐｅ（２，０）ｗｉｔｈｔｈｅｆｏｌｌｏｗｉｎｇｃｏｎｄｉ－ｔｉｏｎｓ：（１）（（ｘｙ）（ｘｚ））（ｚｙ）＝０；（２）（ｘ（ｘｙ））ｙ＝０；（３）ｘｘ＝０；（４）ｘｙ＝ｙｘ＝０ｉｍｐｌｉｅｓｘ＝ｙ．ＩｆａＢＣＩ－ａｌｇｅｂｒａ（Ｘ，，０）ｓａｔｉｓｆｉｅｓ（５）０ｘ＝０．ｔｈｅｎｉｔｉｓｃａｌｌｅｄａＢＣＫ－ａｌｇｅｂｒａ．ＩｎａＢＣＩ－ａｌｇｅｂｒａ，ｔｈｅｆ…