论文标题
理想空间：戒指结构空间的扩展
Ideal spaces: An extension of structure spaces of rings
论文作者
论文摘要
可以为一个任意的戒指理想类别有一个结构空间型理论吗？本文介绍的理想空间允许进行此类研究，我们的理论包括（但不限于）Prime，最大，最小的素数，不可还原，不可还原，完全不可还原，完全不可约，适当，最小，最小，nil，NIL，NIL，NILPOTENT，NILPOTENT，NILPOTENT，NILPOTENT，NILPOTINT，RADER，自由基，原理，原理，有限的，有限的理想。我们表征了清醒的理想空间。我们介绍了强烈断开空间的概念，并表明对于零雅各布森自由基的环，强烈断开的理想空间，该空间包含环的所有最大理想，暗示着环中的非平凡式元素。我们还提供了足够的条件，可以连接频谱。
Can there be a structure space-type theory for an arbitrary class of ideals of a ring? The ideal spaces introduced in this paper allows such a study and our theory includes (but not restricted to) prime, maximal, minimal prime, strongly irreducible, irreducible, completely irreducible, proper, minimal, primary, nil, nilpotent, regular, radical, principal, finitely generated ideals. We characterise ideal spaces that are sober. We introduce the notion of a strongly disconnected spaces and show that for a ring with zero Jacobson radical, strongly disconnected ideal spaces containing all maximal ideals of the ring imply existence of non-trivial idempotent elements in the ring. We also give a sufficient condition for a spectrum to be connected.
