28 citations · 162 across the 42 of their papers we have counts for
57 papers
Almost subtractive submonoids of additive monoids and related quadratic forms
Zur Izhakian, Manfred Knebusch
We introduce and study the class of almost subtractive submonoids of additive monoids. This property relaxes the strict condition of subtractivity while still allowing for a simula…
Supertropical Monoids III: Factorization and splitting covers
Zur Izhakian, Manfred Knebusch
The category of supertropical monoids, whose morphisms are transmissions, has the full--reflective subcategory of commutative semirings. In this setup, quotients…
Archimedean classes in additive monoids
Zur Izhakian, Manfred Knebusch
Summand absorbing submodules are common in modules over (additively) idempotent semirings, for example, in tropical algebra. A submodule of is summand absorbing, if $x + y…
Stratifications of the ray space of a tropical quadratic form by Cauchy-Schwartz functions
Zur Izhakian, Manfred Knebusch
Classes of an equivalence relation on a module V over a supertropical semiring, called rays, carry the underlaying structure of "supertropical trigonometry" and thereby a version o…
Subordinate quadratic forms and isometric maps over semirings
Zur Izhakian, Manfred Knebusch
The paper expands the theory of quadratic forms on modules over a semiring R, introduced in [12]-[14], especially in the setup of tropical and supertropical algebra. Isometric line…
Amalgamation and extensions of summand absorbing modules over a semiring
Zur Izhakian, Manfred Knebusch
A submodule of is summand absorbing, if implies for any . Such submodules often appear in modules over (additively) idempot…