We investigate ideal-semisimple and congruence-semisimple semirings. We give several new characterizations of such semirings using e-projective and e-injective semimodules. We extend several characterizations of semisimple rings to (not necessarily subtractive) commutative semirings.

中文翻译：

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在半单半环上

我们研究理想半简单和同余半简单半环。我们使用 e-projective 和 e-injective semimodules 给出了这种半环的几个新特征。我们将半单环的几个特征扩展到（不一定是减法）交换半环。