Amalgamation and extensions of summand absorbing modules over a semiring

DOI10.1142/S0219498822501249OpenAlexW3126941574MaRDI QIDQ5863514

Manfred Knebusch, Zur Izhakian

Publication date: 1 June 2022

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.06215

zbMATH Keywords

extensionindecomposabledirect sum decompositionamalgamationsemiringlacking zero sumsfree (semi) moduleprojective (semi) modulesemidirect complement

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Projective and free modules and ideals in commutative rings (13C10) Projective techniques in algebraic geometry (14N05) Semirings (16Y60) Ordered semigroups and monoids (06F05) Ordered rings, algebras, modules (06F25) Foundations of tropical geometry and relations with algebra (14T10)

Cites Work

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• Supertropical semirings and supervaluations
• Semigroup identities in the monoid of two-by-two tropical matrices.
• Decompositions of modules lacking zero sums
• Tropical plactic algebra, the cloaktic monoid, and semigroup representations
• Summand absorbing submodules of a module over a semiring
• Supertropical algebra
• Tropical Arithmetic and Matrix Algebra
• Quasilinear convexity and quasilinear stars in the ray space of a supertropical quadratic form
• Generation of summand absorbing submodules
• Monoid Valuations and Value Ordered Supervaluations

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