diff --git a/.travis.yml b/.travis.yml
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,98 +1,141 @@
+# This Travis job script has been generated by a script via
+#
+#   make_travis_yml_2.hs 'algebra.cabal'
+#
+# For more information, see https://github.com/hvr/multi-ghc-travis
+#
 language: c
 sudo: false
 
+git:
+  submodules: false  # whether to recursively clone submodules
+
 cache:
   directories:
-    - $HOME/.cabsnap
     - $HOME/.cabal/packages
+    - $HOME/.cabal/store
 
 before_cache:
   - rm -fv $HOME/.cabal/packages/hackage.haskell.org/build-reports.log
-  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/00-index.tar
+  # remove files that are regenerated by 'cabal update'
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/00-index.*
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/*.json
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/01-index.cache
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/01-index.tar
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/01-index.tar.idx
 
+  - rm -fv $HOME/.cabal/packages/head.hackage
+
 matrix:
   include:
-    - env: CABALVER=1.24 GHCVER=7.4.2
-      compiler: ": #GHC 7.4.2"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-7.4.2,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
-    - env: CABALVER=1.24 GHCVER=7.6.3
-      compiler: ": #GHC 7.6.3"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-7.6.3,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
-    - env: CABALVER=1.18 GHCVER=7.8.4
-      compiler: ": #GHC 7.8.4"
-      addons: {apt: {packages: [cabal-install-1.18,ghc-7.8.4,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
-    - env: CABALVER=1.22 GHCVER=7.10.3
-      compiler: ": #GHC 7.10.3"
-      addons: {apt: {packages: [cabal-install-1.22,ghc-7.10.3,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
-    - env: CABALVER=1.24 GHCVER=8.0.1
-      compiler: ": #GHC 8.0.1"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-8.0.1,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
-    - env: CABALVER=1.24 GHCVER=head
-      compiler: ": #GHC head"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-head,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.4.2"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-7.4.2], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.6.3"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-7.6.3], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.8.4"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-7.8.4], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.10.3"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-7.10.3], sources: [hvr-ghc]}}
+    - compiler: "ghc-8.0.1"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-8.0.1], sources: [hvr-ghc]}}
+    - compiler: "ghc-8.0.2"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-8.0.2], sources: [hvr-ghc]}}
+    - compiler: "ghc-8.2.1"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-8.2.1], sources: [hvr-ghc]}}
+    - compiler: "ghc-8.2.2"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-8.2.2], sources: [hvr-ghc]}}
+    - compiler: "ghc-8.4.1"
+      env: GHCHEAD=true
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-8.4.1], sources: [hvr-ghc]}}
+    - compiler: "ghc-head"
+      env: GHCHEAD=true
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-head], sources: [hvr-ghc]}}
 
   allow_failures:
-    - env: CABALVER=1.24 GHCVER=head
+    - compiler: "ghc-8.4.1"
+    - compiler: "ghc-head"
 
 before_install:
- - unset CC
- - export HAPPYVER=1.19.5
- - export ALEXVER=3.1.4
- - export PATH=~/.cabal/bin:/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:/opt/happy/$HAPPYVER/bin:/opt/alex/$ALEXVER/bin:$PATH
+  - HC=${CC}
+  - HCPKG=${HC/ghc/ghc-pkg}
+  - unset CC
+  - "PATH=/opt/ghc/bin:/opt/ghc-ppa-tools/bin:$PATH"
 
 install:
- - cabal --version
- - echo "$(ghc --version) [$(ghc --print-project-git-commit-id 2> /dev/null || echo '?')]"
- - if [ -f $HOME/.cabal/packages/hackage.haskell.org/00-index.tar.gz ];
-   then
-     zcat $HOME/.cabal/packages/hackage.haskell.org/00-index.tar.gz >
-          $HOME/.cabal/packages/hackage.haskell.org/00-index.tar;
-   fi
- - travis_retry cabal update
- - "sed -i  's/^jobs:.*$/jobs: 2/' $HOME/.cabal/config"
- - cabal install --only-dependencies --enable-tests --enable-benchmarks --dry -v > installplan.txt
- - sed -i -e '1,/^Resolving /d' installplan.txt; cat installplan.txt
-
-# check whether current requested install-plan matches cached package-db snapshot
- - if diff -u installplan.txt $HOME/.cabsnap/installplan.txt;
-   then
-     echo "cabal build-cache HIT";
-     rm -rfv .ghc;
-     cp -a $HOME/.cabsnap/ghc $HOME/.ghc;
-     cp -a $HOME/.cabsnap/lib $HOME/.cabsnap/share $HOME/.cabsnap/bin $HOME/.cabal/;
-   else
-     echo "cabal build-cache MISS";
-     rm -rf $HOME/.cabsnap;
-     mkdir -p $HOME/.ghc $HOME/.cabal/lib $HOME/.cabal/share $HOME/.cabal/bin;
-     cabal install --only-dependencies --enable-tests --enable-benchmarks;
-     if [ "$GHCVER" = "7.10.3" ]; then cabal install Cabal-1.22.4.0; fi;
-   fi
-
-# snapshot package-db on cache miss
- - if [ ! -d $HOME/.cabsnap ];
-   then
-      echo "snapshotting package-db to build-cache";
-      mkdir $HOME/.cabsnap;
-      cp -a $HOME/.ghc $HOME/.cabsnap/ghc;
-      cp -a $HOME/.cabal/lib $HOME/.cabal/share $HOME/.cabal/bin installplan.txt $HOME/.cabsnap/;
-   fi
+  - cabal --version
+  - echo "$(${HC} --version) [$(${HC} --print-project-git-commit-id 2> /dev/null || echo '?')]"
+  - BENCH=${BENCH---enable-benchmarks}
+  - TEST=${TEST---enable-tests}
+  - INSTALLED=${INSTALLED-true}
+  - GHCHEAD=${GHCHEAD-false}
+  - travis_retry cabal update
+  - "sed -i.bak 's/^jobs:/-- jobs: 2/' ${HOME}/.cabal/config"
+  - rm -fv cabal.project.local
+  - "printf 'packages: \".\"\\n' > cabal.project"
+  # Overlay Hackage Package Index for GHC HEAD: https://github.com/hvr/head.hackage
+  - |
+    if $GHCHEAD; then
+      echo 'allow-newer: *:base, *:template-haskell' >> cabal.project
+      echo 'repository head.hackage' >> cabal.project
+      echo '   url: http://head.hackage.haskell.org/' >> cabal.project
+      echo '   secure: True' >> cabal.project
+      echo '   root-keys: 07c59cb65787dedfaef5bd5f987ceb5f7e5ebf88b904bbd4c5cbdeb2ff71b740' >> cabal.project
+      echo '              2e8555dde16ebd8df076f1a8ef13b8f14c66bad8eafefd7d9e37d0ed711821fb' >> cabal.project
+      echo '              8f79fd2389ab2967354407ec852cbe73f2e8635793ac446d09461ffb99527f6e' >> cabal.project
+      echo '   key-threshold: 3' >> cabal.project
+    fi
+  - cat cabal.project
+  - if $GHCHEAD; then cabal new-update head.hackage -v; fi
+  - rm -f cabal.project.freeze
+  - cabal new-build -w ${HC} ${TEST} ${BENCH} --project-file="cabal.project" --dep -j2 all
+  - cabal new-build -w ${HC} --disable-tests --disable-benchmarks --project-file="cabal.project" --dep -j2 all
+  - rm -rf "."/.ghc.environment.* "."/dist
+  - DISTDIR=$(mktemp -d /tmp/dist-test.XXXX)
 
 # Here starts the actual work to be performed for the package under test;
 # any command which exits with a non-zero exit code causes the build to fail.
 script:
- - cabal configure --enable-tests -v2  # -v2 provides useful information for debugging
- - cabal build   # this builds all libraries and executables (including tests)
- - cabal test
- - cabal bench || true  # expected result: these will crash
- - cabal sdist || true  # tests that a source-distribution can be generated
+  # test that source-distributions can be generated
+  - (cd "." && cabal sdist)
+  - mv "."/dist/algebra-*.tar.gz ${DISTDIR}/
+  - cd ${DISTDIR} || false
+  - find . -maxdepth 1 -name '*.tar.gz' -exec tar -xvf '{}' \;
+  - "printf 'packages: algebra-*/*.cabal\\n' > cabal.project"
+  # Overlay Hackage Package Index for GHC HEAD: https://github.com/hvr/head.hackage
+  - |
+    if $GHCHEAD; then
+      echo 'allow-newer: *:base, *:template-haskell' >> cabal.project
+      echo 'repository head.hackage' >> cabal.project
+      echo '   url: http://head.hackage.haskell.org/' >> cabal.project
+      echo '   secure: True' >> cabal.project
+      echo '   root-keys: 07c59cb65787dedfaef5bd5f987ceb5f7e5ebf88b904bbd4c5cbdeb2ff71b740' >> cabal.project
+      echo '              2e8555dde16ebd8df076f1a8ef13b8f14c66bad8eafefd7d9e37d0ed711821fb' >> cabal.project
+      echo '              8f79fd2389ab2967354407ec852cbe73f2e8635793ac446d09461ffb99527f6e' >> cabal.project
+      echo '   key-threshold: 3' >> cabal.project
+    fi
+  - cat cabal.project
+  # this builds all libraries and executables (without tests/benchmarks)
+  - cabal new-build -w ${HC} --disable-tests --disable-benchmarks all
 
-# Check that the resulting source distribution can be built & installed.
-# If there are no other `.tar.gz` files in `dist`, this can be even simpler:
-# `cabal install --force-reinstalls dist/*-*.tar.gz`
- - SRC_TGZ=$(cabal info . | awk '{print $2;exit}').tar.gz &&
-   (cd dist && cabal install --force-reinstalls "$SRC_TGZ")
+  # Build with installed constraints for packages in global-db
+  - if $INSTALLED; then echo cabal new-build -w ${HC} --disable-tests --disable-benchmarks $(${HCPKG} list --global --simple-output --names-only | sed 's/\([a-zA-Z0-9-]\{1,\}\) */--constraint="\1 installed" /g') all | sh; else echo "Not building with installed constraints"; fi
 
+  # build tests & benchmarks
+  - cabal new-build -w ${HC} ${TEST} ${BENCH} all
+  # cabal new-test FAILS if there is no test-suite at all;
+  # so we first test if there is any test-suite by --dry-run,
+  # and, if there is any, then we actually run it.
+  - |
+    if cabal new-test -w ${HC} all --dry-run; then
+      cabal new-test -w ${HC} all;
+    else
+      echo "No test-suite found.";
+    fi
+  # The same applies for benchmarks, but we've ignored them before switching to new-build...
+  - cabal new-bench -w ${HC} all || true
 
+  - rm -rf ./dist-newstyle
+
 notifications:
   irc:
     channels:
@@ -100,3 +143,6 @@
     skip_join: true
     template:
       - "\x0313algebra\x03/\x0306%{branch}\x03 \x0314%{commit}\x03 %{build_url} %{message}"
+
+# REGENDATA ["algebra.cabal"]
+# EOF
diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,7 @@
+4.3.1
+-----
+* Compatibility with GHC 8.4.x: added `Semigroup (End r)` instance.
+
 4.3
 ---
 * Compatibility with GHC 8.0.x
diff --git a/algebra.cabal b/algebra.cabal
--- a/algebra.cabal
+++ b/algebra.cabal
@@ -1,6 +1,6 @@
 name:          algebra
 category:      Math, Algebra
-version:       4.3
+version:       4.3.1
 license:       BSD3
 cabal-version: >= 1.6
 license-file:  LICENSE
@@ -14,7 +14,8 @@
 description:   Constructive abstract algebra
 build-type:    Simple
 tested-with:   GHC == 7.4.2, GHC == 7.6.3, GHC == 7.8.4,
-               GHC == 7.10.3, GHC == 8.0.1
+               GHC == 7.10.3, GHC == 8.0.1, GHC == 8.0.2,
+               GHC == 8.2.1, GHC == 8.2.2, GHC == 8.4.1
 extra-source-files:
   .ghci
   .gitignore
diff --git a/src/Numeric/Ring/Endomorphism.hs b/src/Numeric/Ring/Endomorphism.hs
--- a/src/Numeric/Ring/Endomorphism.hs
+++ b/src/Numeric/Ring/Endomorphism.hs
@@ -10,11 +10,14 @@
 import Numeric.Algebra
 import Prelude hiding ((*),(+),(-),negate,subtract)
 import Data.Proxy
+import Data.Semigroup (Semigroup((<>)))
 
 -- | The endomorphism ring of an abelian group or the endomorphism semiring of an abelian monoid
 -- 
 -- http://en.wikipedia.org/wiki/Endomorphism_ring
 newtype End a = End { appEnd :: a -> a }
+instance Semigroup (End r) where
+  (End a) <> (End b) = End (a . b)
 instance Monoid (End r) where
   mappend (End a) (End b) = End (a . b)
   mempty = End id
