Abstract:We survey theory developed over the past 10 years of semirings which need not be additively cancellative. The main features are a specified ``null ideal'' $\mcA_0$ of a semiring $\mcA,$ taking the place of a zero element, and a ``surpassing relation,'' taking the place of equality, which permit generalizations of the classical algebraic theory to polynomials and their roots, algebraic geometry, matrices, linear algebra, varieties, categories, and module theory. The ``pair'' $(\mcA,\mcA_0)$ is studied along the lines of universal algebra.
From: Louis Rowen [view email]
[v1]
Sun, 22 Feb 2026 14:39:30 UTC (45 KB)
[v2]
Mon, 16 Mar 2026 14:30:48 UTC (45 KB)
[v3]
Wed, 10 Jun 2026 06:05:28 UTC (46 KB)
[v4]
Fri, 26 Jun 2026 04:53:55 UTC (46 KB)
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