南昌大学学报(理科版)
南昌大學學報(理科版)
남창대학학보(이과판)
JOURNAL OF NANCHANG UNIVERSITY(NATURAL SCIENCE)
2014年
2期
103-106
,共4页
半环%实理想%实素理想%实根%广义实根
半環%實理想%實素理想%實根%廣義實根
반배%실이상%실소이상%실근%엄의실근
semiring%semireal ideal%real ideal%real prime ideal%real radical%generalized real radical
在交换半环范畴中引进和研究理想的实根,从而将实代数学中有关结果推广到交换半环上。如下结果被建立:在半环中,一个理想的实根恰等于包含该理想的所有实理想的交集,并也恰等于包含该理想的所有实素理想的交集。此外,形式更为一般的理想的实根--广义实根被考虑,并获得相应的结果。
在交換半環範疇中引進和研究理想的實根,從而將實代數學中有關結果推廣到交換半環上。如下結果被建立:在半環中,一箇理想的實根恰等于包含該理想的所有實理想的交集,併也恰等于包含該理想的所有實素理想的交集。此外,形式更為一般的理想的實根--廣義實根被攷慮,併穫得相應的結果。
재교환반배범주중인진화연구이상적실근,종이장실대수학중유관결과추엄도교환반배상。여하결과피건립:재반배중,일개이상적실근흡등우포함해이상적소유실이상적교집,병야흡등우포함해이상적소유실소이상적교집。차외,형식경위일반적이상적실근--엄의실근피고필,병획득상응적결과。
The notion of real radicals of ideals was introduced in the category of commutative semirings. Similar to the category of commutative rings,the following resultwere established:The real radical of an i-deal in a commutative semiring was the intersection of real ideals,with this ideal being inclusive,and also was the intersection of real prime ideals containing this one.Moreover,a kind of generalized real radicals of ideals was investigated too in the category of commutative semirings,and the corresponding result was ob-tained.