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.
作者
王永铎
李孟高
WANG Yong-duo;LI Meng-gao(School of Science,Lanzhou University of Technology,Lanzhou 730050,Gansu,China)
出处
《西北师范大学学报（自然科学版）》
CAS
北大核心
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)。
关键词
类乘法半模
类余乘法半模
次半模
素半模
素理想
multiplication-like semimodule
comultiplication-like semimodule
second semimodule
prime semimodule
prime ideal
