In the first part , we proof that tensor product of projective semimodules is still projective ; in second part , we construct the equivalence condition of projective semimodule and horn exact sequence 摘要第一部分在[ 3 ]中張量積的定義下證明了投射半模的張量積仍是投射的;第二部分在文獻(xiàn)[ 4 ]正合列的定義下建立了投射半模與函子正合列的等價(jià)條件。
Furthermore , we define a star semimodule and a star subsemimodule ( a subset of m with absorbing property for the operations " + " , " o " ) . based on this , we introduce star congruences and discuss the homomorphic theorem and some properties of star subsemimodules of m about semimodule homomorphisms . in the end , we construct the free star semimodule over a semiring with a unit 進(jìn)一步地,我們定義了星半模以及對(duì)“ + ”和“ ”都具有吸收性的半模m的子集? ?星子半模,在此基礎(chǔ)上我們引入了半模的星同態(tài)和星半模同態(tài)以及星同余等概念,討論了半模的同態(tài)定理以及星子半模關(guān)于半模同態(tài)的一些性質(zhì)