multiplicative subset

noun

A subset of a ring which contains the ring’s unity and which is multiplicatively closed, i.e., it is closed with respect to the ring’s multiplicative operation.

“If P is a proper prime ideal of a ring and M is the set complement, w.r.t. the ring, of P, then M is a multiplicative subset.”

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Meanings

nounmultiplicative subset (plural multiplicative subsets)

plural multiplicative subsets

  1. commutative algebraA subset of a ring which contains the ring’s unity and which is multiplicatively closed, i.e., it is closed with respect to the ring’s multiplicative operation.

    If P is a proper prime ideal of a ring and M is the set complement, w.r.t. the ring, of P, then M is a multiplicative subset.

Cite this entry
APA

multiplicative subset. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/multiplicative%20subset

MLA

“multiplicative subset.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/multiplicative%20subset. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “multiplicative subset,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/multiplicative%20subset.

Source: multiplicative subset on Wiktionary, CC BY-SA 4.0.