对偶半模与自反半模

本文在半模范畴中建立了对偶半模与自反半模的概念，并把模范畴中有关模的对偶性与自反性的结果完整地推广到半模范畴中。     

$D_4$型李代数包络代数旋模的范畴化

本文我们定义复数域$C$上一般线性李代数${\rm gl}_n$ BGG 范畴的若干子范畴及其上的投射函子,利用这些子范畴和投射函子范畴化了$D_4$型李代数包络代数旋模的$n$-次张量积.     

半模的投射盖和半模的根

引入了半模的投射盖和半模的根的初步的定义，给出了半模范畴中投射盖和根的几个初步的结果，推广了模的投射盖和根的一些性质．     

Monoidal Entwined模范畴上的张量积恒等式

本文研究了monoidal entwined模范畴上的张量积恒等式.利用了monoidal entwined模范畴的性质及Doi-Hopf模范畴上的张量积恒等式的研究方法,获得了monoidal entwined模范畴上的一些张量积恒等式,并证明了entwined模范畴有足够的内射对象,结果推广了Doi-Hopf模范畴的结论.     

格序模的f—复盖

J.Martinez首先利用同调的方法研究了格序结构,讨论了偏序模的张量积.W.Powell和A.Bigard分别在1981年和1973年研究了格序模的自由对象,描述了自由f—模的结构.作者推广并且改进了他们的工作,讨论了格序模的f—张量积.本文讨论格序模的f—模复盖,给出复盖函子,f—张量积函子和嵌入函子的关系.     

L-fuzzy模范畴中的极限

本文给出了L-fuzzy模范畴中的极限有点式和无点式刻画,讨论了L-fuzzy模范畴中极限的存在性、唯一性和结构性定理,并得到了极限函子与常量系统函子的伴随性。     

L—fuzzy模范畴的张量积与张量函子

本文在Ｌ—ｆｕｚｚｙ模范畴中，建立了相应的张量积，给出了它的结构性、存在性与唯一性定理，并讨论了张量函子与Ｈｏｍ函子的伴随性。所得结果为通常张量积的“良好推广”（ｇｏｏｄｅｘｔｅｎｓｉｏｎ）。     

函子范畴上加性函子的一个表示

研究函子范畴ModC上加性函子的表示,把一个Abel群作成范畴ModC上的一个左C-模,构造出一个Hom函子和一个函子态射,证明了从函子范畴ModC到范畴Ab的任意变和为积的反变左正合可加函子都与某个Hom函子自然等价.所得结论在函子范畴上,推广了Watts定理.     

可积模的权

本文定义了Ｋａｃ－Ｍｏｏｄｙ代数的一个新的可积模范畴，并且给出了一个可积模是否属于这个模范畴的一个判别准则．另外还详细研究了这个模范畴中的可积模的权系。特别我们定义了虚权和实权。还详细地计算了一些模的虚权和实权，还给出了双曲型广义Ｃａｒｔａｎ矩阵的新刻划．这使我们能够计算一些双曲型Ｋａｃ－Ｍｏｏｄｙ代数的可积模的权。     

可分半群的张量积

本文建立交换可分半群范畴中的张量积,证明其存在与唯一性,同时,建立交换半群的极大可分半群象与张量积之间的关系。最后证明交换可分半群量积的极大半格象同构于其极大半格象的张量积。     

On Flat Semimodules over Semirings

The following analog of the characterization of flat modules has been obtained for the variety of semimodules over a semiring R: A semimodule _RA is flat (i.e., the tensor product functor – A preserves all finite limits) iff A is L-flat (i.e., A is a filtered colimit of finitely generated free semimodules). We also give new (homological) characterizations of Boolean algebras and complete Boolean algebras within the classes of distributive lattices and Boolean algebras, respectively, which solve two problems left open in [14]. It is also shown that, in contrast with the case of modules over rings, in general for semimodules over semirings the notions of flatness and mono-.atness (i.e., the tensor product functor – A preserves monomorphisms) are different.     

Wreath Product of Set-Valued Functors and Tensor Multiplication

Considering the wreath product functor $G wr H:{\cal A} wr^G{\cal B} \rightarrow \SET$ of functors $G: {\cal A}\rightarrow \SET$ and $H: {\cal B}\rightarrow \SET$ over small categories $ {\cal A}$ and $ {\cal B}$, we prove that if tensor multiplication by the functor $G\wrr H$ preserves $ {\cal D}$-limits, where ${\cal D}$ is a small category, then tensor multiplication by $G$ preserves ${\cal D}$-limits, and if tensor multiplication by the functor $G wr H$ preserves ${\cal D}$-limits of representables then tensor multiplications by $G$ and $H$ preserve $ {\cal D}$-limits of representables. We also study flatness and pullback flatness of the wreath product of set-valued functors.     

伪i-内射半模

主要引进了伪i-内射半模的定义,并根据对偶原则,参照k-投射半模及内射模的结论,得到了伪i-内射半模的一些很好的性质,从而实现了把环中内射模的某屿性质在半环中内射半模方面的部分推广.     

拟主k-投射半模(英文)

In this paper,we principally introduce the concept of quasiprincipally k-projective semimodules,on the basis of the theories of k-projective semimodules and quasi-principally modules,we get some good properties of quasi-principally k-projective semimodules,therefore generalize some properties of quasi-principally modules of ring and k-projective semimodules of semiring to quasi-principally k-projective semimodules of semiring.     

AN ANALOGUE OF KüNNETH THEOREM INSTRONG HOMOLOGY

1 IntroductiouLet G and Z be an abelian group and the set Of all integers respectively And letC = (C., ft,', I') denote an inverse system of chain complexes C. and chain maPS I..1: Cv, -Ct,7 5 T' indexed by a directed set r. Strong homology groups HP(C) of the inverse systemC were defilled by J. T. Lisica and S. Mardedie[n. Using the ANRresOlution[9'l1I, algebraictopolOgists defined the strong homology group HP(X; G) of a topological space X with coefficient8 in G and gave exMPl…     

AN ANALOGUE OF KǘNNETH THEOREM IN STRONG HOMOLOGY

After defining the strong tensor product of strong (sub)chain complexes, it is shown that an analogue of the Kunneth theorem holds in strong homology by proving that the kernel (cokernel) of connecting homomorphisms is isomorphic to the direct sum of torsion (tensor) products of strong homology groups. An isomorphism between strong (r-stage) homology groups of inverse systems is also constructed.     

Ni-内射半模及其性质

主要引进了Ni-内射半模的概念,并结合环中N-内射模与半环中内射半模的性质,得到了关于Ni-内射半模的一些性质,这些性质是内射模与内射半模性质的推广.     

Tensor Products and Preservation of Weighted Limits,for S-Posets

We prove that the functor of tensor multiplication by a right S-poset (S is a pomonoid) preserves all small weighted limits if and only if this S-poset is cyclic and projective. We also show that this functor preserves all finite pie-limits if and only if the S-poset is a filtered colimit of S-posets isomorphic to S _S .     

Some remarks on tensor products and flatness of semimodules

Using a restrictive notion of exactness and the natural tensor product, we generalize several results related to flat modules over rings to flat semimodules over semirings.