论文标题
准标记单位代数
Quasi-projective monounary algebras
论文作者
论文摘要
Wu和Jans引入了准标准模块，他们说$ \ cal r $模块$ \ cal m $如果对于每个subpodule $ \ cal n $，则对于每个同粒子$ f：{\ cal m} m} \ rightarrow {\ cal m}/{\ cal n} $有一个$ \ cal m $的内态$ ϕ $，以便$ ϕ \ circ j = f $。我们说，如果对于每个同构$ f：{\ cal s} \ rightarrow {\ cal t} $，则是每个结构$ \ cal t $的结构，如果对于每个结构$ \ cal t $ $ ϕ \ circ j = f $。 2004年，D.Jakubíková-Studenovská定义了由$ {\ cal a}/{\ cal b} $表示的因子代数的概念，其中$ {\ cal a} $是单一的代数和$ {\ cal b} $ {\ cal b} $ subalgebra as subalgebra of $ \ cal a $。在本文中，我们表征了任意基本的准主体单位代数，以定义D.Jakubíková-Studenovská和第二个定义。
Wu and Jans introduced quasi-projective modules where they say a $\cal R$ module $\cal M$ is quasi-projective if for every submodule $\cal N$, for every homomorphism $f : {\cal M} \rightarrow {\cal M}/{\cal N}$ and every epimorphism $j: {\cal M}\rightarrow {\cal M}/{\cal N}$ there is an endomorphism $ϕ$ of $\cal M$ such that $ϕ\circ j=f$. We say that a structure $\cal S$ is quasi-projective if for every structure $\cal T$, for every homomorphism $f : {\cal S} \rightarrow {\cal T}$ and every epimorphism $j: {\cal S}\rightarrow {\cal T}$ there is an endomorphism $ϕ$ of $\cal S$ such that $ϕ\circ j=f$. In 2004 D. Jakubíková-Studenovská defined the concept of the factor algebra denoted by ${\cal A}/{\cal B}$, where ${\cal A}$ is a monounary algebra and ${\cal B}$ is a subalgebra of $\cal A$. In this paper, we characterise the quasi-projective monounary algebras of arbitrary cardinalities for the definition of D. Jakubíková-Studenovská and for the second definition.
