TY - JOUR
AU - Basheyeva, A. O.
PY - 2018/08/27
Y2 - 2024/10/13
TI - Quasivarieties of commutative rings
JF - Journal of Mathematics, Mechanics and Computer Science
JA - JMMCS
VL - 97
IS - 1
SE - Mathematics
DO - 10.26577/jmmcs-2018-1-485
UR - https://bm.kaznu.kz/index.php/kaznu/article/view/485
SP - 54-66
AB - <p>The work is devoted to the problem of undecidability of quasi-equational theories and to the<br>problem of finite axiomatizability. In 1966, Tarsky poded the following problem: Is there an algorithm<br>deciding if the equational theory of a finite set of finite structures is finitely axiomatizabile?<br>In 1986, Maltsev asked the following question: Are there finitely based semigroups, groups, and<br>rings with the undecidable equational theory? Nurakunov A.M. (Nurakunov, 2012) established<br>the existence of continuum many quasivarieties of unars, for which the quasi-equational theory is<br>undecidable and the finite membership problem is also undecidable. In in the paper (Basheyeva,<br>2017), some results in this direction are obtained for graphs, differential gruppoids, and pointed<br>Abelian groups. In the present paper, we prove analogous results for the variety of commutative<br>rings with unit. We prove also that the quasivariety of commutative rings with unit contains continuum<br>many of subquasivarieties with the undecidable quasi-equational theoryб for which the<br>finite membership problem is also undecidable. Apart from trhat, we prove here that the quasivariety<br>of commutative rings with unit contains continuum many subquasivarieties which have an<br>!-independent quasi-equational basis but does not have an indepen</p>
ER -