<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.4 20241031//EN"
        "https://jats.nlm.nih.gov/publishing/1.4/JATS-journalpublishing1-4.dtd">
<article  article-type="research-article"        dtd-version="1.4">
            <front>

                <journal-meta>
                                    <journal-id></journal-id>
            <journal-title-group>
                                                                                    <journal-title>Erzincan University Journal of Science and Technology</journal-title>
            </journal-title-group>
                                        <issn pub-type="epub">2149-4584</issn>
                                                                                            <publisher>
                    <publisher-name>Erzincan Binali Yildirim University</publisher-name>
                </publisher>
                    </journal-meta>
                <article-meta>
                                        <article-id pub-id-type="doi">10.18185/erzifbed.633463</article-id>
                                                                <article-categories>
                                            <subj-group  xml:lang="en">
                                                            <subject>Engineering</subject>
                                                    </subj-group>
                                            <subj-group  xml:lang="tr">
                                                            <subject>Mühendislik</subject>
                                                    </subj-group>
                                    </article-categories>
                                                                                                                                                        <title-group>
                                                                                                                        <article-title>Nilpotent Product of Parafree Lie Algebras and A Basis of This Product</article-title>
                                                                                                                                                                                                <trans-title-group xml:lang="en">
                                    <trans-title>Nilpotent Product of Parafree Lie Algebras and A Basis of This Product</trans-title>
                                </trans-title-group>
                                                                                                    </title-group>
            
                                                    <contrib-group content-type="authors">
                                                                        <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0001-7151-8534</contrib-id>
                                                                <name>
                                    <surname>Velioglu</surname>
                                    <given-names>Zehra</given-names>
                                </name>
                                                                    <aff>HARRAN ÜNİVERSİTESİ</aff>
                                                            </contrib>
                                                                                </contrib-group>
                        
                                        <pub-date pub-type="pub" iso-8601-date="20200831">
                    <day>08</day>
                    <month>31</month>
                    <year>2020</year>
                </pub-date>
                                        <volume>13</volume>
                                        <issue>2</issue>
                                        <fpage>917</fpage>
                                        <lpage>922</lpage>
                        
                        <history>
                                    <date date-type="received" iso-8601-date="20191015">
                        <day>10</day>
                        <month>15</month>
                        <year>2019</year>
                    </date>
                                                    <date date-type="accepted" iso-8601-date="20200530">
                        <day>05</day>
                        <month>30</month>
                        <year>2020</year>
                    </date>
                            </history>
                                        <permissions>
                    <copyright-statement>Copyright © 2008, Erzincan University Journal of Science and Technology</copyright-statement>
                    <copyright-year>2008</copyright-year>
                    <copyright-holder>Erzincan University Journal of Science and Technology</copyright-holder>
                </permissions>
            
                                                                                                <abstract><p>In this work, n-th nilpotent andminimal nilpotent products of parafree Lie algebras are examined and it isshown that these products are parafree. Also, a base set is obtained for then-th nilpotent products of two abelian Liealgebras that are nilpotent of class n.In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of  two abelian Lie algebras that are nilpotent of class n.In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of  two abelian Lie algebras that are nilpotent of class n.</p></abstract>
                                                                                                                                    <trans-abstract xml:lang="en">
                            <p>In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of two abelian Lie algebras that are nilpotent of class n.In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of two abelian Lie algebras that are nilpotent of class n.In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of two abelian Lie algebras that are nilpotent of class n.</p></trans-abstract>
                                                            
            
                                                            <kwd-group>
                                                    <kwd>Parafree Lie algebras</kwd>
                                                    <kwd>  Free Lie Algebras</kwd>
                                                    <kwd>  Nlpotent Product</kwd>
                                            </kwd-group>
                                                        
                                                                            <kwd-group xml:lang="en">
                                                    <kwd>Parafree Lie algebras</kwd>
                                                    <kwd> </kwd>
                                                    <kwd>  Free Lie Algebras</kwd>
                                                    <kwd>  Nilpotent product</kwd>
                                            </kwd-group>
                                                                                                            </article-meta>
    </front>
    <back>
                            <ref-list>
                                    <ref id="ref1">
                        <label>1</label>
                        <mixed-citation publication-type="journal">Akdoğan, N., 2014. Serbest Lie Cebirlerinin Çarpımları ve Rezidülü-P Cebirleri, Master Thesis, Çukurova Uni., Adana.</mixed-citation>
                    </ref>
                                    <ref id="ref2">
                        <label>2</label>
                        <mixed-citation publication-type="journal">Baumslag, G., Groups with the same lower central sequence as a relatively free group I. The groups, Trans. Amer. Math. Soc., 129, 308-321, 1967.</mixed-citation>
                    </ref>
                                    <ref id="ref3">
                        <label>3</label>
                        <mixed-citation publication-type="journal">Baumslag, G., Groups with the same lower central sequence as a relatively free group. II Properties, Trans. Amer. Math. Soc., 142, 507-538, 1969.</mixed-citation>
                    </ref>
                                    <ref id="ref4">
                        <label>4</label>
                        <mixed-citation publication-type="journal">Baur, H., Parafreie Lie algebren und homologie, Diss. Eth Nr., 6126, 1978.</mixed-citation>
                    </ref>
                                    <ref id="ref5">
                        <label>5</label>
                        <mixed-citation publication-type="journal">Golovin, O.N. 1950, Nilpotent Product of Groups. Mat. Sb. (N.S.), 27(69):3, 427-454.</mixed-citation>
                    </ref>
                                    <ref id="ref6">
                        <label>6</label>
                        <mixed-citation publication-type="journal">Velioğlu, Z., 2013. Paraserbest Lie Cebirleri, Ph.D Thesis, Çukurova Uni., Adana.</mixed-citation>
                    </ref>
                                    <ref id="ref7">
                        <label>7</label>
                        <mixed-citation publication-type="journal">Velioğlu, Z., and Ekici, N., 2019, Paraserbest Lie Cebirlerinin Metabelyen Çarpımı, 2-Simetrik Kelimeler ve Verbal Altcebir, Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12(2), 771-777.</mixed-citation>
                    </ref>
                                    <ref id="ref8">
                        <label>8</label>
                        <mixed-citation publication-type="journal">Velioğlu, Z., 2019, Soluble Product of Parafree Lie algebras and Its Residual Properties, Applied Mathematics and Nonlinear Sciences,  4(1) , 1–5.</mixed-citation>
                    </ref>
                            </ref-list>
                    </back>
    </article>
