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Title

J-ARMENDARIZ RINGS RELATIVE TO A MONOID

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Abstract

 FOR A MONOID M, WE INTRODUCE J-M-ARMENDARIZ RINGS, WHICH IS A COMMON GENERALIZATION OF J-ARMENDARIZ AND WEAK M-ARMENDARIZ RINGS, AND INVESTIGATE THEIR PROPERTIES.WE SHOW THAT EVERY NI-RING IS J-M-ARMENDARIZ, FOR ANY UNIQUE PRODUCT MONOID M. ALSO, WE PROVIDE VARIOUS EXAMPLES AND CLASSIFY HOW THE J-M-ARMENDARIZ RINGS BEHAVE UNDER VARIOUS RING EXTENSIONS. IT IS SHOWN THAT IF R IS SEMICOMMUTATIVE RING AND M-ARMENDARIZ THEN R IS J- (MXN) -ARMENDARIZ, WHERE N IS A UNIQUE PRODUCT MONOID.

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