论文标题
交换环与逻辑的一些代数之间的连接
Connections between commutative rings and some algebras of logic
论文作者
论文摘要
在本文中，使用了一些残留晶格的某些次变量之间的连接，我们研究了理想和统一环中理想晶格的某些特性。我们为$ id（a）$是MV-Elgebra，Heyting代数或Boolean代数，我们提供了新的特征，其中$ id（a）$是$ id（a）$，我们在这些类型的戒指之间建立了连接。我们对有限案例非常感兴趣，我们介绍了统计数据。我们表明，形式$ a =％\ mathbb {z} _ {k_ {1}} \ times \ times \ mathbb {z} _ {k__ {k_ {2}} \ times \ times \ times \ times \ mathbb {z}％_ {k_ $ k_ {i} = p_ {i}^{α_{i}} $和$ p_ {i} $一个素数，对于所有$ i \ in \ in \ {1,2，...，r \}，$ \ is bool angeean代数或mv-algebra（不是BOOLEAN）。 使用此结果，我们在有限的交换环中生成了与理想晶格相关的二进制块代码，并提出了一种新的方法，以使用环生成全部（最多达到同构）有限的MV-Elgebras。
In this paper using the connections between some subvarieties of residuated lattices, we investigated some properties of the lattice of ideals in commutative and unitary rings. We give new characterizations for commutative rings $A$ in which $Id(A)$ is an MV-algebra, a Heyting algebra or a Boolean algebra and we establish connections between these types of rings. We are very interested in the finite case and we present summarizing statistics. We show that the lattice of ideals in a finite commutative ring of the form $A=% \mathbb{Z}_{k_{1}}\times \mathbb{Z}_{k_{2}}\times ...\times \mathbb{Z}% _{k_{r}},$ where $k_{i}=p_{i}^{α_{i}}$ and $p_{i}$ a prime number, for all $i\in \{1,2,...,r\},$ \ is a Boolean algebra or an MV-algebra (which is not Boolean). Using this result we generate the binary block codes associated to the lattice of ideals in finite commutative rings and we present a new way to generate all (up to an isomorphism) finite MV-algebras using rings.
