{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T09:27:09Z","timestamp":1773221229495,"version":"3.50.1"},"reference-count":34,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:p> An algebra is entropic if its basic operations are homomorphisms. The paper is focused on representations of such algebras. We prove the following theorem: An entropic algebra without constant basic operations which satisfies so called Szendrei identities and such that all its basic operations of arity at least two are surjective is a subreduct of a semimodule over a commutative semiring. Our theorem is a straightforward generalization of Je\u017eek's and Kepka's theorem for groupoids. As a consequence we obtain that a mode (entropic and idempotent algebra) is a subreduct of a semimodule over a commutative semiring if and only if it satisfies Szendrei identities. This provides a complete solution to the problem in mode theory asking for a characterization of modes which are subreducts of semimodules over commutative semirings. In the second part of the paper we use our theorem to show that each entropic cancellative algebra is a subreduct of a module over a commutative ring. It extends a theorem of Romanowska and Smith about modes. <\/jats:p>","DOI":"10.1142\/s0218196709005470","type":"journal-article","created":{"date-parts":[[2010,1,28]],"date-time":"2010-01-28T10:30:36Z","timestamp":1264674636000},"page":"1025-1047","source":"Crossref","is-referenced-by-count":4,"title":["EMBEDDING ENTROPIC ALGEBRAS INTO SEMIMODULES AND MODULES"],"prefix":"10.1142","volume":"19","author":[{"given":"M. M.","family":"STRONKOWSKI","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Warsaw, Poland"},{"name":"Eduard \u010cech Center, Charles University, Prague, Czech Republic"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"N-ary Quasigroups","author":"Belousov V. 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