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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Tropical semimodules of dimension two
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by Ya. Shitov
St. Petersburg Math. J. 26 (2015), 341-350
Published electronically: February 3, 2015


The tropical arithmetic operations on $\mathbb {R}$ are defined as $a\oplus b=\min \{a,b\}$ and $a\otimes b=a+b$. In the paper, the concept of a semimodule is discussed, which is rather ill-behaved in tropical mathematics. The semimodules $S\subset \mathbb {R}^n$ having topological dimension two are studied and it is shown that any such $S$ has a finite weak dimension not exceeding $n$. For a fixed $k$, a polynomial time algorithm is constructed that decides whether $S$ is contained in some tropical semimodule of weak dimension $k$ or not. This result provides a solution of a problem that has been open for eight years.
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Bibliographic Information
  • Ya. Shitov
  • Affiliation: National Research University–Higher School of Economics, Myasnitskaya Ulitsa 20, Moscow 101000, Russia
  • MR Author ID: 864960
  • Email:
  • Received by editor(s): June 27, 2013
  • Published electronically: February 3, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: St. Petersburg Math. J. 26 (2015), 341-350
  • MSC (2010): Primary 15A03, 15A23, 15A80
  • DOI:
  • MathSciNet review: 3242042