Abstract

We introduce enlargements of rings as additive analogues of enlargements of semigroups. For example, a full matrix ring over an idempotent ring is an enlargement of that ring. As our main result we prove that two idempotent rings are Morita equivalent if and only if they have a joint enlargement. We also give a necessary and sufficient condition for a ring with left local units to be Morita equivalent to a ring with identity. That condition means that a ring is an enlargement of its local subring.

中文翻译：

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戒指的扩大

摘要

我们介绍了环的扩大作为半群扩大的加法类似物。例如，幂等环上的全矩阵环是该环的放大。作为我们的主要结果，我们证明两个幂等环在且仅当它们具有共同扩大量时才与森田等效。我们还提供了一个必要的充分条件，使具有左本地单位的环与森塔等同于具有标识的环。这种情况意味着环是其局部子环的扩大。