类乘法半模和类余乘法半模  

Multiplication-like semimodules and comultiplication-like semimodules

作　　者：王永铎[1] 李孟高 WANG Yong-duo;LI Meng-gao(School of Science,Lanzhou University of Technology,Lanzhou 730050,Gansu,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《西北师范大学学报（自然科学版）》2023年第2期18-22,26,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11861043)。

摘　　要：作为类乘法模和类余乘法模的真推广,引入了类乘法半模和类余乘法半模的概念.设S是交换半环,M是S-半模.若对M的任意非零子半模N,有Ann_(S)(M)Ann_(S)(M/N),则称M是类乘法S-半模;若对任意真subtractive子半模N,有Ann_(S)(M)Ann_(S)(N),则称M是类余乘法S-半模.讨论了类乘法半模与类余乘法半模的性质;证明了M是次S-半模当且仅当对M的任意真subtractive子半模N,Ann_(S)(M/N)=Ann_(S)(M)当且仅当P=Ann_(S)(M)是S的素理想且M是可除S/P-半模;证明了类乘法半模是semi-hopfian半模且类余乘法半模是semi-cohopfian半模.As proper generalizations of multiplication-like modules and comultiplication-like modules,the concepts of multiplication-like semimodules and comultiplication-like semimodules are introduced in this paper.Let S be a commutative semiring and M be an S-semimodule.M is said to be a multiplication-like S-semimodule if Ann _(S)(M)Ann _(S)(M/N)for each nonzero subsemimodule N;M is said to be a comultiplication-like S-semimodule if Ann _(S)(M)Ann _(S)(N)for each proper subtractive subsemimodule N.Some properties of multiplication-like semimodules and comultiplication-like semimodules are discussed.It is proved that M is a second S-semimodule if and only if Ann _(S)(M/N)=Ann _(S)(M)for each proper subtractive subsemimodule N of M if and only if P=Ann _(S)(M)is a prime ideal of S and M is a divisible S/P-semimodule.Furthermore,it is proved that multiplication-like semimodules are semi-hopfian semimodules and comultiplication-like semimodules are semi-cohopfian semimodules.

关 键 词：类乘法半模 类余乘法半模 次半模 素半模 素理想 

分 类 号：O152.7[理学—数学]