1.
Wittrings

1982, Aspects of mathematics=Aspekte der Mathematik, ISBN 9783528085124, Volume 2., xi, 96 p.--

Book

Linear and Multilinear Algebra, ISSN 0308-1087, 2019, pp. 1 - 43

Journal Article

1985, Lecture Notes in Mathematics, ISBN 3540160604, Volume 1173., xvi, 329

Book

Israel Journal of Mathematics, ISSN 0021-2172, 4/2018, Volume 225, Issue 2, pp. 503 - 524

A module over a semiring lacks zero sums (LZS) if it has the property that v +w = 0 implies v = 0 and w = 0. While modules over a ring never lack zero sums,...

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | Research | Zero-sum games | Mathematical research | Decomposition (Mathematics)

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | Research | Zero-sum games | Mathematical research | Decomposition (Mathematics)

Journal Article

International Journal of Algebra and Computation, ISSN 0218-1967, 12/2018, Volume 28, Issue 8, pp. 1633 - 1676

This paper is a sequel of [Z. Izhakian, M. Knebusch and L. Rowen, Supertropical semirings and supervaluations, J. Pure Appl. Algebra 220(1) (2016) 61–93],...

supertropical modules | Tropical algebra | quadratic pairs | supertropicalization | quadratic forms | bilinear forms | CS-ratio | MATHEMATICS

supertropical modules | Tropical algebra | quadratic pairs | supertropicalization | quadratic forms | bilinear forms | CS-ratio | MATHEMATICS

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 08/2019, Volume 223, Issue 8, pp. 3262 - 3294

An R-module V over a semiring R lacks zero sums (LZS) if x+y=0 implies x=y=0. More generally, we call a submodule W of V “summand absorbing” (SA) in V if...

Indecomposable | Semiring | Direct sum decomposition | Upper bound monoid | Lacking zero sums | Projective (semi)module | MATHEMATICS | MATHEMATICS, APPLIED | Algebra

Indecomposable | Semiring | Direct sum decomposition | Upper bound monoid | Lacking zero sums | Projective (semi)module | MATHEMATICS | MATHEMATICS, APPLIED | Algebra

Journal Article

2014, 2014, Lecture Notes in Mathematics, ISBN 9783319032115, Volume 2103, 202

eBook

2002, Lecture notes in mathematics, ISBN 9783540439516, Volume 1791., 267

The present book is devoted to a study of relative Prüfer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to...

Graph labelings | Commutative algebra | Prüfer rings | Commutative Rings and Algebras | Algebraic Geometry | Algebra | Geometry, algebraic

Graph labelings | Commutative algebra | Prüfer rings | Commutative Rings and Algebras | Algebraic Geometry | Algebra | Geometry, algebraic

Book

2010, Algebra and applications, ISBN 9781848822412, Volume 11, 201

The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by...

Forms, Quadratic | Mathematics | Bilinear forms

Forms, Quadratic | Mathematics | Bilinear forms

eBook

Lecture Notes in Mathematics, ISSN 0075-8434, 2014, Volume 2103, pp. 1 - 190

Conference Proceeding

1980, DMV seminar, ISBN 3764312068, Volume 1, 44 p. --

Book

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2016, Volume 507, pp. 420 - 461

This paper is a sequel to [6], in which we introduced quadratic forms on a module over a supertropical semiring R and analyzed the set of bilinear companions...

Supertropical modules | Supertropicalization | Tropical algebra | Bilinear forms | Quadratic forms | Quadratic pairs | Varieties | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRA | MATRICES | ANTIRINGS | Analysis | Algebra

Supertropical modules | Supertropicalization | Tropical algebra | Bilinear forms | Quadratic forms | Quadratic pairs | Varieties | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRA | MATRICES | ANTIRINGS | Analysis | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 10/2014, Volume 416, pp. 200 - 273

Generalizing supertropical algebras, we present a “layered” structure, “sorted” by a semiring which permits varying ghost layers, and indicate how it is more...

Discriminant | Tropical algebra | Polynomial semiring | Resultant | Sylvester matrix | Layered derivatives | Layered supertropical domains | MATHEMATICS | ALGEBRA | Layered supertropic.1 domains | Analysis | Algebra

Discriminant | Tropical algebra | Polynomial semiring | Resultant | Sylvester matrix | Layered derivatives | Layered supertropical domains | MATHEMATICS | ALGEBRA | Layered supertropic.1 domains | Analysis | Algebra

Journal Article

2002, Lecture notes in mathematics, ISBN 9783540439516, Volume 1791., v.

Book

Journal of Pure and Applied Algebra, ISSN 0022-4049, 01/2016, Volume 220, Issue 1, pp. 61 - 93

We initiate the theory of a quadratic form q over a semiring R, with a view to study tropical linear algebra. As customary, one can...

MATHEMATICS | MATRIX ALGEBRA | MATHEMATICS, APPLIED | Algebra

MATHEMATICS | MATRIX ALGEBRA | MATHEMATICS, APPLIED | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2015, Volume 43, Issue 8, pp. 3207 - 3248

We complement two papers on supertropical valuation theory ([11], [12]) by providing natural examples of m-valuations (= monoid valuations), and afterwards of...

Bipotent semirings | Ordered supertropical semirings | and homomorphic equivalence relations | Valuation theory | Lattices | Supervaluations | Secondary: 03G10, 06B23, 12K10, 14T05 | Supertropical algebra | Transmissive | Monoid valuations | Primary: 13A18, 13F30, 16W60, 16Y60 | CMC SUBSETS | MATHEMATICS | Transmissive, and homomorphic equivalence relations | COMMUTATIVE RING | SUPERTROPICAL MATRIX ALGEBRA

Bipotent semirings | Ordered supertropical semirings | and homomorphic equivalence relations | Valuation theory | Lattices | Supervaluations | Secondary: 03G10, 06B23, 12K10, 14T05 | Supertropical algebra | Transmissive | Monoid valuations | Primary: 13A18, 13F30, 16W60, 16Y60 | CMC SUBSETS | MATHEMATICS | Transmissive, and homomorphic equivalence relations | COMMUTATIVE RING | SUPERTROPICAL MATRIX ALGEBRA

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2015, Volume 43, Issue 5, pp. 1807 - 1836

We generalize the constructions of layered domains † to layered semirings, in order to enrich the structure, and in particular to provide finite examples for...

Primary 06F05, 06F20, 14T05, 14T99, 16Y60 | Tropical algebra | Valued monoids | Tropicalization | Tropical categories | Secondary 06F25, 12K10 | Tropical geometry | Valuations | 06F20 | COMMUTATIVE RING | 16Y60 | 12K10 | MATHEMATICS | Primary 06F05 | MATRIX ALGEBRA | 14T99 | 14T05 | Secondary 06F25

Primary 06F05, 06F20, 14T05, 14T99, 16Y60 | Tropical algebra | Valued monoids | Tropicalization | Tropical categories | Secondary 06F25, 12K10 | Tropical geometry | Valuations | 06F20 | COMMUTATIVE RING | 16Y60 | 12K10 | MATHEMATICS | Primary 06F05 | MATRIX ALGEBRA | 14T99 | 14T05 | Secondary 06F25

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2010, Volume 138, Issue 1, pp. 75 - 84

We give a complete list of all quadratic modules and inclusions between them in the ring R[[X]] of formal power series in one variable X over a euclidean field...

Geometry | Squares | Algebra | Mathematical theorems | Mathematical sets | Mathematical rings | Polynomials | Automorphisms | Power series | Formal power series rings | Quadratic modules | Preorderings | preorderings | MATHEMATICS | MATHEMATICS, APPLIED | formal power series rings

Geometry | Squares | Algebra | Mathematical theorems | Mathematical sets | Mathematical rings | Polynomials | Automorphisms | Power series | Formal power series rings | Quadratic modules | Preorderings | preorderings | MATHEMATICS | MATHEMATICS, APPLIED | formal power series rings

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2013, Volume 266, Issue 1, pp. 43 - 75

The objective of this paper is to lay out the algebraic theory of supertropical vector spaces and linear algebra, utilizing the key antisymmetric relation of...

Change of base semirings | Tropical algebra | Linear and bilinear forms | Supertropical vector spaces | Linear algebra | Gram matrix | MATHEMATICS | change of base semirings | linear and bilinear forms | tropical algebra | supertropical vector spaces | linear algebra

Change of base semirings | Tropical algebra | Linear and bilinear forms | Supertropical vector spaces | Linear algebra | Gram matrix | MATHEMATICS | change of base semirings | linear and bilinear forms | tropical algebra | supertropical vector spaces | linear algebra

Journal Article

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